Deck 8: Contingent Payments

Question 1

The random walk theory of stock prices states that price movements in disjoint time periods are independent of each other.The probability that the value of a portfolio of stocks invested in companies listed on the TSE300 rises in any one year is 0.60.What is the probability that the portfolio's value moves in the same direction in both of the next 2 years?

A)0.06
B)0.36
C)0.52
D)0.96

Answer 1

0.52

Question 2

A hydro company finds that 80% of its customers pay a given monthly bill in full.Suppose 2 customers are chosen at random from the list of all customers.What is the probability that at least one of the two customers will pay their next monthly bill in full?

A)0.32
B)0.64
C)0.80
D)0.96

Answer 2

0.96

Question 3

For a $1 ticket,a lottery offers the following prizes:
•1 prize of $50,000
•10 prizes of $10,000
•100 prizes of $100
•4000 prizes of 5 free ticket
If 250,000 tickets are sold,what is the expectation per ticket?

A)0.55
B)0.64
C)0.70
D)0.72

Answer 3

0.70

Question 4

Recent statistics show that the stock market (as measured by the TSE index)goes up in a day about 60% of the time and goes down the other 40% of the time.Statistics also show that if the market goes up one day,then it goes up the next day 70% of the time and down 30% of the time.But if the market goes down one day,then it goes up the next day 80% of the time and down 20% of the time.What is the probability that in three consecutive days,the market goes up for two of the days and down for one of the days?

A)49.4%
B)43.2%
C)37.8%
D)14.4%

Question 5

A 6-sided die has been weighted so that 5 or 6 comes up 3 times as often as 1 or 2.Also,3 or 4 comes up 2 times as often as 1 or 2.Player A wins $6 if 1 comes up,$5 if 2 comes up and $4 if 3 comes up.Player B wins $3 if 4 comes up,$2 if 5 comes up and $1 if 6 comes up.What is the value of E[A] - E[B],where E[A] is the expectation of winning for player A and E[B] is the expectation of winning for player B?

A)0.33
B)0.67
C)-0.67
D)-0.33

Question 6

Recent statistics show that the stock market (as measured by the TSE index)goes up in a day about 60% of the time and goes down the other 40% of the time.Statistics also show that if the market goes up one day,then it goes up the next day 70% of the time and down 30% of the time.But if the market goes down one day,then it goes up the next day 80% of the time and down 20% of the time.What is the probability that in two consecutive days,the market goes in the opposite direction?

A)24%
B)32%
C)48%
D)50%

Question 7

You are given that 7.2% of the American population has Type O-negative blood.If 5 people are randomly selected to give blood,what is the probability that at least one of them has Type O-negative blood?

A)0.688
B)0.622
C)0.312
D)0.928

Question 8

Recent statistics show that the stock market (as measured by the TSE index)goes up in a day about 60% of the time and goes down the other 40% of the time.Statistics also show that if the market goes up one day,then it goes up the next day 70% of the time and down 30% of the time.But if the market goes down one day,then it goes up the next day 80% of the time and down 20% of the time.What is the probability that in three consecutive days,the market goes in the same direction (either up or down)on each day?

A)35.1%
B)31.0%
C)28.4%
D)28.0%

Question 9

Suppose that to get a job offer,you need to take 2 exams.The results of your exam are independent and you have 70% to pass each of them.If you fail both exams,you will have no chance to get the job.If you pass one of them,you will have 30% chance to get the job.If you pass both exams,you will have an 80% chance to get the job.What is the probability that you get the job?

A)0.392
B)0.455
C)0.518
D)0.812

Question 10

You have two bags of marbles that have the following content:
Bag 1: 6 red,4 white Bag 2: 6 red,3 white
You reach into bag 1 (without looking),take out one marble and put it into bag 2.Then you reach into bag 2 and take out one marble.What is the probability that the marble chosen from bag 2 is red?

A)0.42
B)0.60
C)0.66
D)0.70

Question 11

The probabilities that bond A,B,C and D will pay every one of their coupons along with the redemption value are 50%,70%,80% and 60% respectively.What is the probability that at least three of the bonds will fully meet their obligations?

A)39.4%
B)56.2%
C)85.6%
D)98.8%

Question 12

While driving from his house to work each day,Jack Hammer passes 3 stoplights.If the probability of getting a red light is 1/3 for each of the 3 lights,what is the probability that Jack hits at least one red light?

A)7/27
B)8/27
C)9/27
D)19/27

Question 13

A fair standard die is rolled until a six appears.If X is the number of rolls that are necessary.What is the probability that X ≤ 2?

A)12/36
B)11/36
C)7/36
D)6/36

Question 14

Recent statistics show that the stock market (as measured by the TSE index)goes up in a day about 60% of the time and goes down the other 40% of the time.Statistics also show that if the market goes up one day,then it goes up the next day 70% of the time and down 30% of the time.But if the market goes down one day,then it goes up the next day 80% of the time and down 20% of the time.What is the probability that in two consecutive days,the market goes in the same direction (either up or down)on both days?

A)62%
B)52%
C)50%
D)42%

Question 15

A 6-sided die has been weighted so that 5 or 6 comes up 3 times as often as 1 or 2.Also,3 or 4 comes up 2 times as often as 1 or 2.Player A wins $6 if 1 comes up,$5 if 2 comes up and $4 if 3 comes up.Player B wins $3 if 4 comes up,$2 if 5 comes up and $1 if 6 comes up.Player B wins $3 if a 4 comes up,$2 if a 5 comes up and $1 if a 6 comes up.What is player B's expected winnings?

A)$1.25
B)$1.67
C)$1.75
D)$2.50

Question 16

A fair coin is tossed 4 times.Event A is the probability that there are no heads and Event B is that probability that there are no tails.What is the probability of (Event A or Event B)?

A)0.0625
B)0.1250
C)0.1875
D)0.2500

Question 17

A game show gives contestants 5 questions with 3 possible answers and awards $10 for every correct answer.If a contestant answers all 5 questions correctly,they win an extra $500.What is the probability of a contestant who guesses at every question will get at least 2 questions correct?

A)0.54
B)0.46
C)0.40
D)0.33

Question 18

When John and Carl play a game,John wins,on average,2 out of every 5 games played.Today they agree to play until John wins one game or until three games have been played,whichever comes first.What is the probability that John wins one game today?

A)0.432
B)0.480
C)0.720
D)0.784

Question 19

A student has 3 exams.The probability that he does "well" on his first exam is 80%.However,his performance on the remaining two exams depends on how "well" he did on the previous exam.The probability of doing "well" on an exam is 95% if the previous exam was done "well",but only 50% if the previous was not done "well".What is the probability he does "well" on exactly 2 of his 3 exams?

A)15.3%
B)27.8%
C)32.7%
D)38.4%

Question 20

One day,20 people show up at a baseball diamond,13 males and 7 females.Since only 18 people are required to form two teams,two people are to be chosen at random to be the referees (umpires).What is the probability that one of them is male and one is female?

A)22.75%
B)23.95%
C)45.50%
D)47.89%

Question 21

Students who take drivers education have a 2% probability of having an accident in their first year of driving,while students who do not take drivers education have a 10% probability.Statistics show that the average cost of an accident is $8500.Statistics also show that 70% of new drivers have taken drivers education.What is the expected cost of an accident per driver in their first year of driving?

A)$119
B)$374
C)$646
D)$1020

Question 22

An individual age 50 is promised a payment of $8,000 if he is alive at age 55.If he dies within the next 5 years,his estate will get ½ of this amount,payable at the time that he would have turned 55.You are given the probability of a 50 year old surviving to age 55 is 0.9464.If the interest rate is i = 5%,how much will it cost this individual to buy this payment scheme?

A)$5932.23
B)$6100.22
C)$7571.20
D)$7785.60

Question 23

Students who take drivers education have a 3% probability of having an accident in their first year of driving,while students who do not take drivers education have a 9% probability.Statistics show that the average cost of an accident is $7000.Statistics also show that x% of new drivers have taken drivers education.If the expected cost of an accident per driver in their first year of driving is $394.80,what is the value of x?

A)56%
B)53%
C)47%
D)44%

Question 24

A large hat contains five $10 bills,seven $5 bills and ten $1 bills.In a game,you are allowed to reach in and pull two bills at random from the hat.If both bills are of the same denomination,you get to keep both of them.In order to make this a fair game,how much should you pay to participate in this game?

A)$2.46
B)$2.16
C)$3.56
D)$5.08

Question 25

You are considering purchasing a 10-year $10,000 par value bond that pays semi-annual coupons at j₂ = 10%.The probability the n^th coupon will be defaulted,given that the previous (n - 1)coupons were paid,is 5% for each coupon during the first 5-years and 10% for each coupon for the last 5-years.What price should you pay for the bond if the desired yield is j₂ = 8%?

A)$10,220.61
B)$10,425.90
C)$10,882.37
D)$11,610.16

Question 26

A $5000 bond pays interest at j₂ = 4% and is redeemable at par in 5 years.The desired yield is j₂ = 5%.What price should you pay for this bond if the probability of any payment being defaulted is 1%,given that all previous payments were paid?

A)$4792.45
B)$4733.39
C)$4561.24
D)$4362.69

Question 27

A loan is to be repaid with semi-annual payments of $500 for 5 years (first payment 6 months from now).There is a 5% chance of default for any payment and if a payment is defaulted,no further payments will be made.The rate of interest on the loan is j₂ = 9%.Assuming the lender took into account the default rates,how much money was lent out?

A)$3860.87
B)$3758.54
C)$3142.99
D)$3072.28

Question 28

A $5000 bond pays interest at j₂ = 4% and is redeemable at par in 5 years.The desired yield is j₂ = 5%.What price should you pay for this bond if the probability of default in any 6-month period is 1%?

A)$4792.45
B)$4733.39
C)$4561.24
D)$4362.69

Question 29

On the day his child turned age 1,Sam bought a scholarship plan that pays $8000 on the day his child turns 18 but only if his child attends university.The probability of a 1-year old attending university at age 18 is 55%,while the probability of a 1-year old surviving to age 18 is 0.989.If j₁ = 4%,what is a fair price to pay for this scholarship plan (ignoring expenses)?

A)$2148.07
B)$2234.00
C)$2258.84
D)$4351.60

Question 30

Sam and Ella play a dice game which involves throwing two fair die.Sam wins $42 from Ella if the total of the two die is 7 or 9.Otherwise Ella wins $X from Sam.In order for this to be a fair game,what should be the value of X?

A)$5.25
B)$6.77
C)$8.40
D)$16.15

Question 31

A 10-year $5000 par value bond pays interest at j₂ = 7%.The probability that a payment is defaulted,given that all previous payments were made,is 3%.What is the purchase price to yield j₂ = 6%.

A)$3264.29
B)$3482.77
C)$5210.78
D)$5293.83

Question 32

A person,who is currently age 50,invests $A today.She is to receive two payments of $5000,one when she reaches age 55 and the second when she reaches age 60.The first payment is guaranteed,but the second payment is paid only if she is alive at age 60 to collect it.You are given the probability of a 50 year old female surviving to age 55 is 0.9867 and surviving to age 60 is 0.9654.If the interest rate is 4%,what is the value of A?

A)$7487.46
B)$7432.80
C)$7370.58
D)$7315.93

Question 33

When John and Carl play a game,John wins,on average,2 out of every 5 games played.Today they agree to play until Carl wins one game or until three games have been played,whichever comes first.At the end of each game,the loser pays the winner $1.What is Carl's expected winnings?

A)0.264
B)0.312
C)0.504
D)0.936

Question 34

For an investment of $20,000 today at j₂ = 4%,you expect to receive three payments of $R,one each at the end of 1,2 and 3 years.If the probability of default for any payment is 3%,what should the value of R be?

A)$7083.22
B)$7435.51
C)$7656.95
D)$8123.83

Question 35

A large hat contains five $10 bills,seven $5 bills and ten $1 bills.In a game,you are allowed to reach in and pull two bills at random from the hat,putting the first bill back in the hat before choosing the second bill.If both bills are of the same denomination,you get to keep both of them.In order to make this a fair game,how much should you pay to participate in this game?

A)$2.46
B)$3.56
C)$4.32
D)$8.64

Question 36

Upon the birth of her child,Cindy buys a scholarship plan that pays $8000 on the day her child turns 18 and another $8000 on the day her child turns 19 but only if her child goes to university.The probability of a newborn surviving to age 18 is 0.989 and to age 19 is 0.980,while the probability of attending university at age 18 is 55%.If this cost of this scholarship plan is $4500 (ignoring expenses)and j₁ = 4%,what is the probability of going into 2^nd year of university at age 19,given that a person attended university at age 18?

A)0.580
B)0.590
C)0.626
D)0.632

Question 37

A perishable product is purchased by a retailer for $5 and is sold for $7.If an item is not sold during the day,the retailer loses $5.Past history has shown that there is a 30% chance of selling 28 of these products in a day,a 28% chance of selling 29 of them in a day,a 25% chance of selling 30 of them in a day and a 17% chance of selling 31 of them in a day.If you order 30 of the items per day,what is your expected daily profit?

A)$48.04
B)$23.41
C)$18.14
D)‒$13.43

Question 38

A game show gives contestants 5 questions with 3 possible answers and awards $10 for every correct answer.If a contestant answers all 5 questions correctly,they win an extra $500.If a contestant guesses at every question,what is their expected winnings?

A)$5.39
B)$15.39
C)$16.67
D)$18.72

Question 39

For an investment of $20,000 today at j₂ = 4%,you expect to receive three payments of $R,one each at the end of 1,2 and 3 years.The probability of default of the first payment is 3%,while the probability of default of the 2^nd or 3^rd payment,given that the previous payments were made,is 3%.What should the value of R be?

A)$6996.07
B)$7212.44
C)$7429.87
D)$7435.51

Question 40

A 10-year $5000 par value bond pays interest at j₂ = 7%.The probability of default in any 6-month period is 3%.What is the purchase price to yield j₂ = 6%.

A)$3264.29
B)$3482.77
C)$5210.78
D)$5293.83

Question 41

The ABC company lends $A to a person who agrees to pay back $500 at the end of every three months for two years.ABC estimates there is a 2% chance the person will default on a payment,given that all previous payments were made.If the interest rate on the loan is j₄ = 6%,what should be the value of A?

A)$3668.10
B)$3737.98
C)$3742.96
D)$3747.76

Question 42

The ABC company lends $A to a person who agrees to pay back $500 at the end of every three months for two years.ABC estimates there is a 2% chance this person will default on a payment.If the interest rate on the loan is j₄ = 6%,what should be the value of A?

A)$3668.10
B)$3737.98
C)$3742.96
D)$3747.76