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Probability of rolling doubles

Probability of rolling double 3s on a pair of dice

This math skill teaches how to calculate the probability of rolling double threes using two dice. It explores two approaches: multiplying the probability of getting a three on each die and analyzing the ratio of favorable outcomes to total outcomes. Both methods confirm the same probability.

Learn probability of rolling doubles

Teaching Transcript

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What is the chance that we roll double threes on these dice

We can approach this in two ways. One is by looking at the probability of getting a 3 on each die, and realizing that getting a 3 on both is just the intersection of the two probabilities

Which means we would multiply them together. If we had more dice, we would multiply by more of the same.

Each die has a 1 in 6 chance of getting a 3, so we'd multiply 1 over 6 by 1 over 6

So our probability is 1 in 36. Let's solve this another way to make sure it checks out.

We can look at desired outcomes over total outcomes.

There's only 1 way to roll double 3s, given 2 dice, and there are 36 unique ways to roll 2 dice, so we have the same fraction. Similarly for more dice, we would just multiply the denominator by 6 for each additional die.

Of course, we can divide the fraction and show our probability as a decimal or a percent. 1 in 36 is about a 2.8 percent chance.

Skill Practice

Probability of rolling double 3s on a pair of dice

Test your understanding of probability of rolling doubles by practicing it! Work through the below exercises to use it in practice.