Our office of five people has two tickets to tonight's (virtual) Iron Slug and the Slime

concert. The five participants (Fred, Carolyn, Pam, Bob, and Shep) are each going to be assigned

a random number, chosen independently from a continuous uniform distribution over the interval

[0, 1]. An individual is declared to be a winner if their random number exceeds 1/3. If the number

of winners is exactly 2, the tickets are given to those two people. If the number of winners is not

exactly 2, the previous winner's designations are erased, and the procedure is repeated. This game

continues until the tickets are awarded.

Part 1a: What is the probability that on any particular round, the tickets will be awarded?

Part 1b: How many times, on average, must this procedure be repeated before an award is made?

Part 1c: A machine has been programmed to carry out this selection algorithm. As soon as

exactly two winners have been determined the machine announces "We have a winner !!" and then

waits a minute before giving the names of the winners. When "We have a winner !!" is announced

by the machine, what is the probability that Fred will go to the concert?