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Question

An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least 3 successes

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Solution

An experiment succeeds as often as it fails.
Therefore, there are 3 successes and 1 failure.
Thus the probability of success = 13
And the probability of failure = 14
We need to find the probability of atleast 3 successes in the next 5 trials.
Required probability = P(X=3)+P(X=4)+P(X=5)
=5C3p3q2+5C4p4q1+5C5p5q0=5C3(34)3(14)2+5C4(34)4(14)1+5C5(34)5(14)0=10(34)3(14)2+5(34)3(14)2+(34)3(14)29181024=459512=0.896
is the required probability.

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