Problem 175
easy
Three different faces
Three fair dice are rolled. Find the probability that all three show different numbers.
Answer
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
Hints 0/2
Roll the dice one at a time.
The second die must avoid one value, the third must avoid two.
h
Solution
s Shown after a correct answer. Revealing it first marks the problem as seen, not solved.
Idea. Roll the dice one after another and ask each new die to avoid the values already seen.
Step 1. The first die can show anything.
Step 2. The second die differs from the first with probability , and then the third differs from both with probability .
Step 3.
By counting. Of the outcomes, have three different values, and .