For 6 trials of an experiment, let X be a binomial variate which satisfies the relation `9P(X = 4) = P(X = 2)`. Find the probability of success.

Explanation

Let `p` be the probability of success and `q` that of failure in a single trial. Then,

`P(X=r)=6_{C_{r}} p^{r} q^{6-r} `

`9 times 6_{C_{4}} p^{4} q^{2}=6_{C_{2}} p^{2} q^{4} `

`9 p^{2}=q^{2} `

`3 p=q `

`3 p=1-p `

`p=frac{1}{4}`