Kalvin Crook is contemplating a life of crime. If he commits a crime and does not get caught, he stands to gain $80. If he commits a crime and does get caught, he stands to lose $120. He is contemplating a four event crime spree. The probability of getting caught on each day is not a function of whether or not he got caught on the previous day (i.e. the events are independent). Below is a list of the probability of getting caught on each day of crime:
Prday1 Prday2 Prday3 Prday4
Get Caught .2 .3 .2 .4
Go Free .8 .7 .8 .6
a. Calculate Kalvin's expected haul over the four event crime spree.
b. Calculate the probability that Kalvin will never get caught over the four days.
c. Calculate the probability that Kalvin will get caught exactly half the time.
d. Given that Kalvin will get caught exactly two out of four times, calculate his expected haul.
2. Jessica has the following utility of income function: U = 1700Y - .011Y2. Jessica currently has $65,000 and faces a 4% chance of losing $50,000.
a. Calculate Jessica's utility level if she has $65,000.
b. Calculate Jessica's expected income and her expected utility level.
c. Calculate the amount Jessica would be willing to pay to insure against a 4% chance of losing $50,000.
d. Calculate how much Jessica would be willing to pay to insure against a 20% chance of losing $10,000.