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Pepys wrote newton to ask which of three events is more likely: that a person get at least 1 six when 6 dice are rolled

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Final answer:

The likelihood of rolling at least one six with six dice is determined by calculating the complementary probability. The calculation involves finding the probability of not getting a six with all six dice and subtracting this value from 1.

Step-by-step explanation:

The question asks about the likelihood of certain probabilistic events occurring when rolling dice, which is a common problem in the study of probability. Specifically, the student inquires about the case of rolling six dice and the chances of getting at least one six.

To solve this, we should consider the probability of the complementary event—that is, not rolling any six at all with six dice—and subtract this from 1 (which represents certainty or a 100% probability).

The probability of not rolling a six on a single die is ⅕, and because each roll is independent, the probability of not rolling a six on any of the six dice is ⅕6. We calculate this and subtract the result from 1 to obtain the probability of rolling at least one six.

So, the calculation would be 1 - (⅕6), and this gives us the probability that a six will appear at least once when six dice are rolled. This approach is known as calculating the complementary probability.

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