in a certain board game, a player rolls two fair six-sided dice until the player rolls doubles (where the value on each die is the same). the probability of rolling doubles with one roll of two fair six-sided dice is 16. what is the probability that it takes three rolls until the player rolls doubles? responses

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20-12-2022
Mathematics

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in a certain board game, a player rolls two fair six-sided dice until the player rolls doubles (where the value on each die is the same). the probability of rolling doubles with one roll of two fair six-sided dice is 16. what is the probability that it takes three rolls until the player rolls doubles? responses

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abhinavjh321 abhinavjh321 · Answer 1 · 2022-12-24T08:36:59-05:00

The probability of rolling doubles with three rolls of two fair six-sided dice is 0.512.

The probability of rolling doubles with one roll of two fair six-sided dice is 16/36, or 1/6. This means that the probability of not rolling doubles with a single roll is 5/6.

The probability of not rolling doubles with two rolls is (5/6)^2, or 25/36.

The probability of not rolling doubles with three rolls is (5/6)^3, or 125/216.

Therefore, the probability of rolling doubles with three rolls of two fair six-sided dice is (216-125)/216, or 91/216, or 0.512.

P(doubles on 1 roll) = 1/6

P(not doubles on 2 rolls) = (5/6)^2 = 25/36

P(not doubles on 3 rolls) = (5/6)^3 = 125/216

P(doubles on 3 rolls) = 1 - (125/216) = 91/216 = 0.512

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