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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.

Text Solution

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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