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a fair die is rolled repeatedly. let be the number of rolls needed to obtain a 5, and the number of rolls needed to obtain a 6. calculate .

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We would need to find the expected number of rolls. This is an expectation value. We would first need to find the probability of rolling a 5. In this case this would be 1/6. This is because for each roll of the die there is a 1/6 chance of rolling a 5. So we take this probability and we raise it to the power of the number of rolls to find the expectation value of having a five rolled. This would give us the answer 3.33. This would mean that on average 3.33 rolls to get a 5 being rolled.

User Rob Kent
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