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Question

A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.


Solution

When a die  is rolled once, probability of obtaining a six is 16 and that of not obtaining a six is 116=56

Let p=16 and q=56

P (obtaining third six in the sixth throw)

=P(obtaining two sixes in first five throws and a six in the sixth throw)

=P(obtaining two sixes in first five throws)×16

=6C2(16)2(56)3×16=5×41×2×5366=10×12566=62523328

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