jmc

Question

Monica tosses a fair 6-sided die. If the roll is a prime number, then she wins that amount of dollars (so that, for example, if she rolls 3, then she wins 3 dollars). If the roll is composite, she wins nothing. Otherwise, she loses 3 dollars. What is the expected value of her winnings on one die toss? Express your answer as a dollar value to the nearest cent.

Accepted Answer

The only primes on a die are 2, 3, and 5. The only composites are 4 and 6. The only other option is rolling a 1. There is a 16 probability that she will roll a 1 and lose 3, a 13 probability of rolling a composite and winning 0, and a 16 probability of winning each of 2, 3, or 5. So E = 13 0 + 16(2+3+5) + 16 -3 $1.17.