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.
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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.
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What is the chance that we roll double threes on these dice
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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
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Which means we would multiply them together. If we had more dice, we would multiply by more of the same.
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Each die has a 1 in 6 chance of getting a 3, so we'd multiply 1 over 6 by 1 over 6
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So our probability is 1 in 36. Let's solve this another way to make sure it checks out.
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We can look at desired outcomes over total outcomes.
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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.
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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.