This math skill teaches how to calculate the probability of rolling a specific number on a die at least once in two tries, using the concept of the union of probabilities for independent events. It involves adding the probabilities of each event and then subtracting the intersection of the probabilities.
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Probability of rolling a number on a die at least once in two tries
Test your understanding of probability of multiple rolls by practicing it! Work through the below exercises to use it in practice.
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What is the chance of rolling a 5 given two rolls?
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These are independent events since the die doesn't change, and we need either to happen, so the probability of both is the union of the probability of 5, and the probability of 5 again.
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For unions, we add the probabilities, and then subtract the intersection, so we have the probability of 5, plus the probability of 5, minus the probability of 5 times itself.
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Since there is a single 5 on a die, and 6 possible outcomes, the chance of rolling a 5 is 1 in 6.
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So our answer is 11 in 36 as the chance of rolling a 5 given two tries.
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11 in 36 is zero point three zero five five, or about a 30.5 percent chance.