Exam 8: Contingent Payments

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?

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 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 $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%?

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?

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?

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 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 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?

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 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 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?

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?

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%?

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?

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?

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?

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?

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?

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?