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A man performs 10 trials of an experimen...

A man performs 10 trials of an experiment, if the probability of getting '4 sucesses' is maximum, then find the probability of failure in each trial.

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Verified by Experts

The correct Answer is:
`3//5`
Let probability of success in a trial is 'p'
Then `P(X=4)=""^(10)C_(4)P^(4)(1-p)^(6)`
`P(X)""^(10)C_(4)[4p^(3)(1-p)^(6)-6(1-p)^(5)p^(4)]`
`=""^(10)C_(4)p^(3)(1p)^(5)(4-10p)`
For maximum `P(X)=0`
`impliesP(X)=2/5`
`impliesP(X)=3/5`
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