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# Complementary Probability

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What is the probability that when we roll four fair 6-sided dice, they won't all show the same number?

Jul 27, 2022

#1
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https://web2.0calc.com/questions/what-is-the-probability-that-when-we-roll-four-fair-6-sided-dice-they-won-t-all-show-the-same-number

he had a small error simplifying his fraction

Jul 27, 2022
#2
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The probability of rolling the same number on all 4 dice is $$6 \times ({1 \over 6})^4 = {1 \over 216}$$. There are 6 numbers to choose from, and the 4 dice must roll that 1 number.

So, if the probability of failing is $${1 \over 216}$$, what must the probability of success be, knowing the sum of the probability of failing, and the probability of succeeding is always equal to 1?

Jul 27, 2022