Probability problem by Aira Thalca

Probability Level 3

Amina and Albert alternate turns tossing a fair coin. Amina goes first and each player takes three turns. The first player to toss a tail wins. If neither Amina nor Bert tosses a tail, then neither wins. What is the probability that Amina wins?

Give your answer to 3 decimal places.


The answer is 0.65625.

Aira Thalca by Aira Thalca , 24, Indonesia

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1 solution

Aira Thalca
Dec 27, 2016

If Amina wins, she can win on her first turn, second turn, or third turn

If she wins or her first turn, This occurs with probability 1 2 \frac {1}{2}

If she wins on her second turn, This occurs with probability 1 8 \frac {1}{8}

If she wins on her third turn, This occurs with probability 1 32 \frac {1}{32}

Therefore, the probability that Amina wins is 1 2 + 1 8 + 1 32 = 21 32 \frac {1}{2} + \frac {1}{8} + \frac {1}{32} = \frac {21}{32}

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