Browse · MATH
Printjmc
counting and probability intermediate
Problem
Beth rolls a fair six-sided die. If she rolls a prime number, she wins 1 dollar, but if she rolls a composite number, she loses 1 dollar. If she rolls 1 nothing happens. What is the expected value of the amount of money Beth will win if she rolls the die once? Express your answer as a common fraction.
Solution
There are 3 possible prime numbers which can be rolled (2, 3, and 5), and two possible composite numbers which can be rolled (4 and 6). Each number has a chance of being rolled. So, the expected value of Beth's winnings is
Final answer
\frac{1}{6}