Problem 179
easy
An even product
Three fair dice are rolled and the three numbers are multiplied. Find the probability that the product is even.
Answer
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
Hints 0/2
When is a product odd?
A product is odd only if every factor is odd.
h
Solution
s Shown after a correct answer. Revealing it first marks the problem as seen, not solved.
Idea. Use the complement. The product is odd exactly when all three dice are odd.
Step 1. Each die is odd with probability , independently, so all three are odd with probability .
Step 2.
Compare. The sum of three dice is even only half the time: one even die is enough to make the product even, but not the sum.