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Wednesday, August 01, 2018

IIBF EXAM REVIEW : CAIIB ABM 2017 COLLECTION

IIBF EXAM REVIEW : CAIIB ABM 2017 COLLECTION


BM – RECOLLECTED QUESTIONS – PATTERN – JULY 2017
MODULE – A
Chapter
No of Questions
Topic
1 chapter
0
No question asked
2 chapter
2
Demand & supply curve , shifting
3 Chaper
8
Double data table of money supply,
 & cost push inflation
4 Chapter
2
Keynes theory
5 Chapter
1
business cycle
6 Chapter
1
industry based CSO
7 Chapter
0
No question asked
8 Chapter
3
Reverse Repo use, and OMO operation
9 Chapter
2
GDP calculation Numericals
10 Chapter
5
Net Fiscal & Primary Deficit ,Gross Fiscal & Primary Deficit,
 Rev. Deficit . Problem given solve all deficit
11 Chapter
0
No question

MODULE – B
Chapter
No of Questions
Topic
12 chapter
1
Compounding interest
13 chapter
5
Cluster sampling, standard error, standard deviation
14 Chapter
8
One problem based question
15 Chapter
2
One problem baed question time series easy
16 Chapter
1
estimation
17 Chapter
2
Bond value +one theory
18 Chapter
5
Problem based question table format siplex method through
19 Chapter
1
Theory

MODULE – C
Chapter
No of Questions
Topic
20–25 Chapter
5
Case Study

5
Case Study

1
Case Study

9
Other topic :- 360 degree, Personality, HRIS, feedback, Performance
Note:- Question were not in one sequence, they are on random basis.

MODULE – D
Chapter
No of Questions
Topic
26 Chapter
2
Credit Mgm
27 Chapter
12
Ratio Analysis 10 problem based Question & 2 theory based
28 Chapter
4
Problem based
29 Chapter
1
Theory
30 Chapter
1
Theory
31 Chapter
2
Theory
32 Chapter
2
Theory
33 Chapter
2
Theory


1. M0, M1, M2 - 5 questions
2. DER
3. Full table for CR, DER and DSCR (5 que)
4. Many paragraph type from HR (20 appx)
5. Simulation
6. Questions from time value of money
7. One question was for purchase of car by cash 7 lakh or 1.5 lakh for 6 year... 10%
8. Credit audit
9. Real GDP
10. Nominal GDP
11. Net fiscal deficit
12. Net primary deficit
13. Gross fiscal deficit
14. Emotional intelligence
15. Market clearing price
16. LPP
17. 5 marks based on revenue
18. MCLR
19. Inflation 5 marks
20. NWC calculation 5 marks
21. Using simplex method 5 mark
22. Present value
23. Future Value
24. Bond Rate ques 9 mark
Questions 60% theory 40% problems based on theoritical concepts...
Theory part questions:
HRM
Credit management
Buisness mathmematics
.................................................
Problems/Numerical Questions :
Buisness mathematics
Correlation and regression
Linear programing
Profit and loss account
Working capital
GDP deflator
Union budget
Ratio analysis

Interest will be paid on CRR? - No
Commercial papers are issued by - Large banks or large corporate companies
Sarfesi act will be applicable for what amount - Loans with outstanding above Rs 1.00 lac
Budget case study
Time Series 5 qus
Stimulation based 5 qus
5 marks on balance sheet
who's control for market economy
72 is for doubling the investment
working capital finance
Project finance based decision making 5 qus
Case study on corporate financing
Money injected by rbi into economy problems
RBI regulations on lending
What is not a quality of simulation.
Problems on simulation
........................................................
Maslow's Hierarchy of Needs
1. Biological and Physiological needs
2. Safety needs
3. Love and belongingness needs
4. Esteem needs
5. Self-Actualization needs
........................................................
Defition of YTM
Yield to maturity is the discount rate at which the sum of all future cash flows from the bond (coupons and principal) is equal to the price of the bond.
The Yield to maturity (YTM), book yield or redemption yield of a bond or other fixed-interest security, such as gilts, is the internal rate of return (IRR, overall interest rate) earned by an investor who buys the bond today at the market price, assuming that the bond will be held until maturity, and that all coupon and principal payments will be made on schedule.
.........................................................
Types of defaulters
Who has the capacity to pay its dues but does not pay willfully to the Banks/FIs etc.
Who Diverts its funds for its own benefit rather than the benefit of its firm/Company etc.
Who deliberately does not fulfill the purpose of finance i.e. generation of assets to be created out of Bank/FI finance.
Who disposes off or removes its assets without the permission or the knowledge of the Bank/FI.
...............................................................................
Self-Awareness 

Understanding self helps in the process of self-development
Johari Window by Luft and Ingham
The more one knows oneself, the better equipped he is to face challenges



KNOWN TO SELF
NOT KNOWN TO SELF
KNOWN TO OTHERS
ARENA
BLIND
NOT KNOWN TO OTHERS
CLOSED
DARK
........................................................
Case Studies on Ratio Analysis (Quick Ratio, Current Ratio, Inventory Turn over Ratio, DSCR)
XYZ Pvt Ltd has the following assets and liabilities as on 31st March 2016 (in Lakhs) :
Non Current Assets
Goodwill 75
Fixed Assets 75
Current Assets
Cash in hand 25
Cash in bank 50
Short term investments 45
Inventory 25
Receivable 100
Current Liabilities
Trade payables 100
Income tax payables 60
Non Current Liabilities
Bank Loan 50
Deferred tax payable 25
Find the Quick Ratio
Quick Ratio = (Cash in hand + Cash at Bank + Receivables + Marketable Securities) / Current Liabilities
= (25+50+45+100) / 160
= 220 / 160
= 1.38
.................................
Cash = Rs. 100000
Debtors = Rs. 200000
Inventories = Rs. 300000
Current liabilities = Rs. 200000
Total current assets = Rs. 600000
The quick ratio = ?
Since Quick ratio = Quick asset / CL
Here Quick asset = CA - Inventory
Now CA= (Cash + Debtor.....etc ) = Rs. 600000
Here inventories = 300000/-
So, Quick Assets = 600000 - 300000 = Rs. 300000
CL = Rs. 200000
Hence QR = 300000/200000
i.e 1.5:1
.............................................
Current ratio of a unit is 3:1 and quick ratio is 1:1. The level of current assets is Rs 15 lac. What is the amount of quick asset?
Since CR = CA: CL
CR= CA:CL = 3:1
i.e. 15:CL= 3:1
i.e CL = 5 lac
Now QR= 1:1
Since QR= Quick asset/CL ( here quick asset is CA-Inventory )
Hence QA= CL ~ 5 lac
.............................................
A firm has Capital of Rs. 200, Reserve Rs. 230 Term Loan of Rs. 180, Advance from customers Rs. 40, sundry creditor Rs. 100, Bank CC limit balance Rs. 400, Fixed Assets Rs. 300, Preliminary expenses Rs. 80, Debit balance of profit and loss account balance Rs. 30, advance tax paid Rs. 20, cash on hand Rs. 20, Stock Rs. 400 and sundry creditor Rs. 300. on the basis of the above information:
The current ratio would be ......
Current Ratio=Current Assets / Current Liabilities
CA=(20+20+400+300)=740
CL=(40+100+400)=540
= 740/540
= 1.37:1
.........................
Govind's Furniture Company sells industrial furniture for office buildings. During the current year, it reported cost of goods sold on its income statement of 10,00,000. Govind's beginning inventory was 30,00,000 and its ending inventory was 40,00,000. Govind's turnover is ...... times.
Inventory Turnover Ratio = Cost of Goods Sold / Average Inventory
= 1000000 / ((3000000+4000000)/2)
= 1000000 / (7000000/2)
= 1000000 / 3500000
= 0.29 Times
This means that Govind only sold roughly a third of its inventory during the year. It also implies that it would take Govind approximately 3 years to sell his entire inventory or complete one turn. In other words, Govind does not have very good inventory control.
.................................
Raju's Furniture Company sells industrial furniture for office buildings. During the current year, Raju reported cost of goods sold on its income statement of 25,00,000. Raju's beginning inventory was 40,00,000 and its ending inventory was 60,00,000. Calculate Raju's Furniture Company's Inventory Turnover Ratio.
Inventory Turnover Ratio = Cost of goods sold / Average inventory for that period
= 2500000 / ((4000000 + 6000000)/2)
= 2500000 / 5000000
= 0.5
.................................
The amount of term loan instalment is Rs 15000/- per month, Monthly average interest on TL is Rs 10000/-. If the amount of depreciation is Rs 30000/- p.a and PAT is Rs 300000/-. What would be the DSCR?
Since DSCR = (interest + PAT + Depriciation) / ( interest + instalment of TL )
= (10000×12 + 300000 + 30000)/(10000×12 + 15000×12)
= (120000 + 330000) / (120000 + 180000)
= 450000/300000
= 1.5
.............................................
The amount of term loan installment is Rs 15000/- per month, monthly average interest on TL is Rs 7500/-. If the amount of depreciation is Rs 100000/- p.a and PAT is Rs 350000/-. What would be the DSCR?
Since DSCR = (interest + PAT + Depriciation) / (interest + instalment of TL)
DSCR = (7500×12 + 350000 + 100000)/(7500×12 + 15000×12)
= (90000 + 350000 + 100000) / (90000 + 180000)
= 540000 / 270000
= 2
..............
A bank calculates that its individual savings accounts are normally distributed with a mean of Rupees 2,000 and a standard deviation of Rupeess600. If the bank takes a random sample of 100 accounts, what is the probability that the sample mean will lie between Rupees 1,900 and Rupees 2,050?
Standard Error = SD / √(N)
= 600 / √100
= 600 / 10
= 60
Using the equation
z = (x bar minus Mu)/SE
we get 2 z values
for x bar = Rs. 1900,
z = (1900 - 200) / 60
= (-100) / 60
= -1.67
for x bar = Rs. 2050,
z = (2050 - 200) / 60
= 50 / 60
= 0.83
Probability table gives us probability of 0.4525 corresponding to a z value of –1.67, and it gives probability of 0.2967 for a z value of 0.83. If we add these two together, we get 0.7492 as the total probability that the sample mean will lie between Rs. 1900 and Rs. 2,050.
.............................................
A jar contains 3 red marbels, 7 green marbels and 10 white marbles. If a marble is drawn at random, What is the probability that marble drawn is white?
Here Red = 3
Green = 7
White = 10
Hence total sample space is (3+7+10)= 20
Out of 20 one ball is drawn n(S) = {c(20,a.} = 20
To find the probability of occurrence of one White marble out of 10 white ball
n(R)={c(10,a.} = 10
Hence P(R) = n(R)/n(S)
= 10/20 = 1/2
........................................................
We have six students say A, B, C, D, E, F participating in a quiz contest. Out of six students only two can reach to the final. What is the probability of reaching to the final of each student ?
Since out of 6, 2 can reach the final. Hence sample space is
n(S) = 6 c2 = 6!/(6-b.!×2! = 15
Here event of occurrence of probability of each student out of six (A B C D E F) = (AB AC AD AE AF) = n(E) = 5
Now P(E) = 5/15 = 1/3
........................................................
An bag contains 10 black balls and 5 white balls. 2 balls are drawn from the bag one after other without replacement. What is the probability that both drawn are black ?
Let E and F denote respective events that first and second ball drawn are black.
We have to find here P(E), P(E/F) and P(E n F )
Now P(E) = P(Black in first drawn) = 10/15
Also given that the first ball is drawn i.e events E has occurred. Now there are 9 black balls and 5 white balls left in the urn. Therefore the probability that the second ball drawn is black, given that the ball first drawn is black nothing but conditional probability of F given that E has occurred already.
Hence P(E/F) = 9/14
Now by the multiplication rule of probability
P(E n F) = P(E) × P(E/F)
= 10/15 × 9/14 = 3/7
........................................................
A sum of Rs. 32800 is borrowed to be paid back in 2 years by two equal annual installments allowing 5% compound interest. Find the annual payment.
Here,
PV =?
P = Rs. 32800
T = 2 years
R = 5% = 0.05
PV = P / R * [(1+R)^T - 1]/(1+R)^T
32800 = P × (1.052 – 1) ÷ (0.05 × 1.052)
P = 32800 ÷ 1.8594
P = 17640
.............................................
Find Standard Deviation and Coefficient of Variance for the values given : {13,35,56,35,77}
Number of terms (N) = 5
Mean:
Xbar = (13+35+56+35+77)/5
= 216/5
= 43.2
Standard Deviation (SD):
Formula to find SD is
σx= √(1/(N - 1)*((x1-xm)2+(x2-xm)2+..+(xn-xm)2))
=√(1/(5-1)((13-43.2)2+(35-43.2)2+(56-43.2)2+(35-43.2)2+(77-43.2)2))
=√(1/4((-30.2)2+(-8.2)2+(12.9)2+(-8.2)2+(33.8)2))
=√(1/4((912.04)+(67.24)+(163.84)+(67.24)+(1142.44)))
=√(588.2)
=24.2528
Coefficient of variation (CV)
CV = Standard Deviation / Mean
= 24.2528/43.2
= 0.5614
Hence the required Coefficient of Variation is 0.5614
.............................................
A bank calculates that its individual savings accounts are normally distributed with a mean of Rupees 2,000 and a standard deviation of Rupeess600. If the bank takes a random sample of 100 accounts, what is the probability that the sample mean will lie between Rupees 1,900 and Rupees 2,050?
Standard Error = SD / √(N)
= 600 / √100
= 600 / 10
= 60
Using the equation
z = (x bar minus Mu)/SE
we get 2 z values
for x bar = Rs. 1900,
z = (1900 - 200) / 60
= (-100) / 60
= -1.67
for x bar = Rs. 2050,
z = (2050 - 200) / 60
= 50 / 60
= 0.83
Probability table gives us probability of 0.4525 corresponding to a z value of –1.67, and it gives probability of 0.2967 for a z value of 0.83. If we add these two together, we get 0.7492 as the total probability that the sample mean will lie between Rs. 1900 and Rs. 2,050.
.............................................

Questions on GDP / GNP
Go through the following data and answer the questions (all in Indian Rupees in Crores)
1. Consumptions - Rs. 30000
2. Gross investment - Rs. 40000
3. Govt spending - Rs. 20000
4. Export - Rs. 70000
5. Import - Rs. 60000
6. Taxes - Rs. 5000
7. Subsidies(on production and import) - RS. 1000
8. Compensation of employee - Rs. 500
9. Property Income - Rs. 500
7,8,9 - Net receivable from aboard
10.Total capital gains from overseas investment - Rs. 1500
11.Income earned by foreign national domestically - Rs. 500
Calculate GNP
GDP = Consumption + Gross investment + Government spending + (Exports - Imports)
GDP = C+I+G+(X-M)
= 30000+40000+20000+(70000-60000)
= 100000
GNP=GDP+NR(total capital gains from Overseas investment-income earned by foreign national domestically)
= 100000 + (1500-500)
= 101000
.............................................
Questions on Business Mathematics
Find the present value of quarterly payment of Rs. 250 for 5 years @ 12% compounded quarterly.
Here,
P = Rs. 250
T = 5 years = 5 × 4 = 20 quarters
R = 12% = 12% ÷ 4 = 0.03% quarterly
PV = P / R * [(1+R)^T - 1]/(1+R)^T
PV = 250 × (1.0320 – 1) ÷ (0.03 × 1.0320)
= 3719
.............................................
Mr x is to receive Rs. 10000, as interest on bonds by end of each year for 5 years @ 5% roi. Calculate the present value of the amount he is to receive.
Here,
P = 10000
R = 5% p.a.
T = 5 Y
PV = P / R * [(1+R)^T - 1]/(1+R)^T
PV to be received, if the amount invested at end of each year:
So,
FV = (100000÷0.05) * {(1+0.05)^5 – 1} ÷ (1+0.05)^5
= 43295
.............................................
X opened a recurring account with a bank to deposit Rs. 16000 by the end of each year @ 10% roi. How much he would get at the end of 3rd year?
Here,
P = 16000
R = 10% p.a.
T = 3 yrs
FV = P / R * [(1+R)^T - 1]
FV = 16000 * (1.13 – 1) ÷ 0.1
= 52960
.............................................
Questions on Money Supply
Given,
Currency with public - Rs. 120000 Crores
Demand deposit with banking system - Rs. 200000 Crores
Time deposits with banking system - Rs. 250000 Crores
Other deposit with RBI - Rs. 300000 Crores
Savings deposit of post office savings banks - Rs. 100000 Crores
All deposit with post office savings bank excluding NSCs - Rs. 50000 Crores
Calculate M2.
M1 = currency with public + demand deposit with the banking system + other deposits with RBI
M1 = 120000+200000+300000
M1 = 620000
M2 = M1+Savings deposit of post office savings banks
So,
M2 = 620000+100000
M2 = 720000 Crores
.............................................
Given,
Currency with public - Rs. 120000 Crores
Demand deposit with banking system - Rs. 200000 Crores
Time deposits with banking system - Rs. 250000 Crores
Other deposit with RBI - Rs. 300000 Crores
Savings deposit of post office savings banks - Rs. 100000 Crores
All deposit with post office savings bank excluding NSCs - Rs. 50000 Crores
Calculate broad money M3.
M1 = currency with public + demand deposit with the banking system + other deposits with RBI
M1 = 120000+200000+300000
M1 = 620000
M3 = M1+Time deposit with banking system
So,
M3 = 620000+250000
M3 = 870000 Crores
.............................................
Given,
Currency with public - Rs. 90000 Crores
Demand deposit with banking system - Rs. 180000 Crores
Time deposits with banking system - Rs. 220000 Crores
Other deposit with RBI - Rs. 260000 Crores
Savings deposit of post office savings banks - Rs. 60000 Crores
All deposit with post office savings bank excluding NSCs - Rs. 50000 Crores
Calculate M4.
M4 = M3+All deposit with post office savings bank excluding NSCs
M3 = M1+Time deposit with banking system
M1 = currency with public + demand deposit with the banking system + other deposits with RBI
M1 = 90000+180000+260000
M1 = 530000
So,
M3 = M1+Time deposit with banking system
M3 = 530000+220000
M3 = 750000 Crores
So,
M4 = M3+All deposit with post office savings bank excluding NSCs
M4 = 750000+50000
M4 = 800000 Crores
.....................................................
Questions on Bond/YTM
A bond has been issued with a face value of Rs. 1000 at 10% Coupon for 3 years. The required rate of return is 8%. What is the value of the bond if the Coupon amount is payable on half-yearly basis?
Here,
FV = 1000
CR = 10% half-yearly = 5% p.a.
Coupon = FV × CR = 50
R = 8% yearly = 4% p.a.
t = 3 years
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
= 1052
.............................................
A console bond of Rs. 10000 is issued at 6%. Coupon current interst rates and 9%. Find out the current value of the console bond.
Solution :
= 10000*0.06/0.09
= 6000/0.09
= 6670
.............................................
Suppose you purchased a bond Rs.1000 for Rs.920. The interest is 10 percent, and it will mature in 10 years. Calculate Yield to maturity
C=Coupon payment
F=Face value
P=Price
n=Years to maturity
Yield To Maturity=C+(F-P/n)/(F+P/2)
=100+(1000-920/10)/(1000+920/2)
=100+(80/10)/(1920/2)
=100+8/960
=108/960
=0.1125
=11.25%
.............................................
A bond has been issued with a face value of Rs. 20000 at 12% Coupon for 3 years. The required rate of return is 10%. What is the value of the bond?
Here,
FV = 20000
Coupon Rate (CR) = 0.12
t = 3 yr
R (YTM) = 0.10
Coupon = FV × CR = 2400
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
So, Value of bond = 20995
.............................................
Case Studies on HR
The top management of ABC. Bank was in a triumphant mood after engaging XYZ Ltd, one of the top IT Companies as a consultant for a massive technology upgradation in the Bank. Their enthusiasm was short lived, as the project did not progress well and the consultants were not able to deliver the desired results even after several months. In fact the Consultants were of the view that it may never be possible to implement the project with 100% success as they seemed to be facing resistance from the employees at multi-levels. The employees at all levels seemed reluctant to cooperate. Their fear of Role erosion seemed palpable.
What does “Role erosion” mean in this context?
a. The fear of the employee that he will be sent out
b. Fear that the responsibility and the power will reduce
c. Fear that he will no more be an indispensable
d. a & b
Ans - d
.............................................
The critical issue in this case is:
a. Attitudes of individuals
b. Training of people
c. Group behavior due to a sense of the unknown
d. All the above
Ans - c
.............................................
How could this situation have beenmanaged better?
a. By issuing project details and time frame mentioning punishments in case of delay
b. By roping in the HR professionals to act as coordinator
c. By recognizing that any change brings its own reactions and co-opting the managers even before Consultants moved in
d. b & c
Ans - d
.............................................
The Bank should deal with the employee resistance by:
a. Co-opting the employees
b. Communicating strategically about the potential benefits
c. Conducting simultaneous training to familiarize the staff with the new software
d. All of the above
Ans - d

Meaning of valence in Vroom’s Expectancy Model
Valence is the value a person assigns to his desired reward
...................................................
Annual conpounded 8%. Find,
Quarterly effective ROI - 8/4 = 2%
Monthly effective ROI - 8/12 = 0.666%
...................................................
10% ROI : x amount will become quadruple in how many years.
In Simple Interest - 30 years
In Compound Interest - (7.2+7.2) = 14.4 years
...................................................
Difference between GDP and GNP
GDP = consumption + investment + (government spending) + (exports − imports).
GNP = GDP + NR (Net income inflow from assets abroad or Net Income Receipts) - NP (Net payment outflow to foreign assets).
...................................................
Wealth definition of economics given by - Adam Smith
...................................................
Definition of net working capital
Amount arranged by the enterprise through long term funds (either capital or borrowings) is called Net Working Capital.
Total current assets minus total current liabilities
...................................................
Quik ratio meaning
Quick ratio is calculated by dividing current assets (excluding inventory) by total current liabilities.
...................................................
CPs are issued by - Corporates
...................................................
360 degree appraisal
Under this appraisal system an employee is rated by people who are affected by the performance of the employee and have adequate knowledge about his working and performance. The appraisal is generally done by the seniors, colleagues (peers), subordinates, suppliers, customers and all other stakeholders. It also includes the self-assessment by the employee himself.
...................................................
Revenue receipt and expenditure
Revenue deficit is the excess of revenue expenditure over revenue receipts
...................................................
Narrow Money (M1) is equal to Currency with the public plus Demand deposits with the banking system plus `Other’ deposits with the RBI.
Broad Money (M3) is equal M I plus Time deposits with the banking system

Questions on Propability / Sampling / Standard Deviation, Standard Error, Co-variance
A bank calculates that its individual savings accounts are normally distributed with a mean of Rupees 2,000 and a standard deviation of Rupeess600. If the bank takes a random sample of 100 accounts, what is the probability that the sample mean will lie between Rupees 1,900 and Rupees 2,050?
Standard Error = SD / √(N)
= 600 / √100
= 600 / 10
= 60
Using the equation
z = (x bar minus Mu)/SE
we get 2 z values
for x bar = Rs. 1900,
z = (1900 - 200) / 60
= (-100) / 60
= -1.67
for x bar = Rs. 2050,
z = (2050 - 200) / 60
= 50 / 60
= 0.83
Probability table gives us probability of 0.4525 corresponding to a z value of –1.67, and it gives probability of 0.2967 for a z value of 0.83. If we add these two together, we get 0.7492 as the total probability that the sample mean will lie between Rs. 1900 and Rs. 2,050.
.............................................
A jar contains 3 red marbels, 7 green marbels and 10 white marbles. If a marble is drawn at random, What is the probability that marble drawn is white?
Here Red = 3
Green = 7
White = 10
Hence total sample space is (3+7+10)= 20
Out of 20 one ball is drawn n(S) = {c(20,a.} = 20
To find the probability of occurrence of one White marble out of 10 white ball
n(R)={c(10,a.} = 10
Hence P(R) = n(R)/n(S)
= 10/20 = 1/2
........................................................
We have six students say A, B, C, D, E, F participating in a quiz contest. Out of six students only two can reach to the final. What is the probability of reaching to the final of each student ?
Since out of 6, 2 can reach the final. Hence sample space is
n(S) = 6 c2 = 6!/(6-b.!×2! = 15
Here event of occurrence of probability of each student out of six (A B C D E F) = (AB AC AD AE AF) = n(E) = 5
Now P(E) = 5/15 = 1/3
........................................................
An bag contains 10 black balls and 5 white balls. 2 balls are drawn from the bag one after other without replacement. What is the probability that both drawn are black ?
Let E and F denote respective events that first and second ball drawn are black.
We have to find here P(E), P(E/F) and P(E n F )
Now P(E) = P(Black in first drawn) = 10/15
Also given that the first ball is drawn i.e events E has occurred. Now there are 9 black balls and 5 white balls left in the urn. Therefore the probability that the second ball drawn is black, given that the ball first drawn is black nothing but conditional probability of F given that E has occurred already.
Hence P(E/F) = 9/14
Now by the multiplication rule of probability
P(E n F) = P(E) × P(E/F)
= 10/15 × 9/14 = 3/7
........................................................
A sum of Rs. 32800 is borrowed to be paid back in 2 years by two equal annual installments allowing 5% compound interest. Find the annual payment.
Here,
PV =?
P = Rs. 32800
T = 2 years
R = 5% = 0.05
PV = P / R * [(1+R)^T - 1]/(1+R)^T
32800 = P × (1.052 – 1) ÷ (0.05 × 1.052)
P = 32800 ÷ 1.8594
P = 17640
.............................................
Find Standard Deviation and Coefficient of Variance for the values given : {13,35,56,35,77}
Number of terms (N) = 5
Mean:
Xbar = (13+35+56+35+77)/5
= 216/5
= 43.2
Standard Deviation (SD):
Formula to find SD is
σx= √(1/(N - 1)*((x1-xm)2+(x2-xm)2+..+(xn-xm)2))
=√(1/(5-1)((13-43.2)2+(35-43.2)2+(56-43.2)2+(35-43.2)2+(77-43.2)2))
=√(1/4((-30.2)2+(-8.2)2+(12.9)2+(-8.2)2+(33.8)2))
=√(1/4((912.04)+(67.24)+(163.84)+(67.24)+(1142.44)))
=√(588.2)
=24.2528
Coefficient of variation (CV)
CV = Standard Deviation / Mean
= 24.2528/43.2
= 0.5614
Hence the required Coefficient of Variation is 0.5614
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A bank calculates that its individual savings accounts are normally distributed with a mean of Rupees 2,000 and a standard deviation of Rupeess600. If the bank takes a random sample of 100 accounts, what is the probability that the sample mean will lie between Rupees 1,900 and Rupees 2,050?
Standard Error = SD / √(N)
= 600 / √100
= 600 / 10
= 60
Using the equation
z = (x bar minus Mu)/SE
we get 2 z values
for x bar = Rs. 1900,
z = (1900 - 200) / 60
= (-100) / 60
= -1.67
for x bar = Rs. 2050,
z = (2050 - 200) / 60
= 50 / 60
= 0.83
Probability table gives us probability of 0.4525 corresponding to a z value of –1.67, and it gives probability of 0.2967 for a z value of 0.83. If we add these two together, we get 0.7492 as the total probability that the sample mean will lie between Rs. 1900 and Rs. 2,050.
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Source: internet

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