Imagine a lottery system, where a non-recurring-4-digit number will be chosen at
ID: 3070335 • Letter: I
Question
Imagine a lottery system, where a non-recurring-4-digit number will be chosen at random, i.e., it is not possible for a number with 2 identical digits to be chosen. You can buy up to 5 lottery tickets, where each ticket is associated with a different 4-digit number of your choice. If you bought a ticket with the winning number, then you win $5000. Each lottery ticket costs $1. Assume that you can buy up to 5 lottery tickets because you only have $5.
3a) Assume that you only bought 1 lottery ticket. What is the probability that this ticket has the winning number?
3b) Assume that you are risk-neutral. How many lottery tickets would you buy? Justify your decision using a decision tree for this problem.
3c) Assume that you know the second digit of the winning number is 8 with complete certainty and you bought 1 lottery ticket with 8 as the second digit. What is the probability that this ticket has the winning number?
3d) Assume that you are risk-neutral. Additionally, assume that someone offers to sell you the identity of the second digit of the winning number for $4000. Would you buy that information? Justify your decision using a decision tree for this problem.
Thank you in advance!
Explanation / Answer
3a) Total No of possibilities of 4 digit tickets numbers with no number recurring is 9*9*8*7 = 4536
therfore, if i bought only one lottery ticket, the probabilty that this ticket is the winning ticket is 1/ 4536 = 0.00022045855379
3b) Assuming that i am risk neutral, buying all five lottery tickets would give me the probability of 5/4536 of winning the lottery. i would need to spend 5 dollars worth of money to get those tickets though.
3c) the probability of winning after knowingv the second digit is 8 is 1/504 = 0.00198412698
3d) Assuming that i am risk-neutral. If someone offers to sell me the identity of the second digit of the winning number for $4000, i wouldnt buy that information. since, even after knowing the second digit , my probability of winning the lottery is only 1/504