what is the answer for 5a+4b?

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Updated: 9/27/2023

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Elizabeth Roberts ∙

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What is the probability of observing exactly one 3 when rolling a fair die five times?

Same as for rolling 5 dice at the same time, namely 5 x 1/6 x (5/6)4 This is the second last term in the expansion of (a + b)5 where a is the probability of a die falling at 3 (ie 1/6) and b is the probability of it not falling at 3 (ie 5/6) and the various terms of the expansion correspond to the various combinations : a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5. Which of course adds up to 1 when you allow all possibilities, not just one 3.

what is the answer for 5a+4b?

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What is the probability of observing exactly one 3 when rolling a fair die five times?

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