Question

For 6 trails of an experiment , let x be a binomial variate which satisfies the relation $9P\left(X=4\right)=P\left(X=2\right)$. Find the probability of success.

• A. $\frac{1}{5}$
• B. $\frac{1}{4}$
• C. $\frac{5}{4}$
• D. $\frac{3}{4}$

Answer 1

Answer: (B)

$\frac{1}{4}$

Let P be probably of success and q be probability of failure, Therefore

$P(x\times 4)=9{\times }^6{C}_4\left(P{)}^4\right(q{)}^2{=}^6{C}_2\left(p{)}^2\right(q{)}^4=P(x=2)$

$\frac{9\times 6!}{4!2!}(p{)}^2=\frac{6!}{4!2!}{q}^2$

Since, $p+q=1$

$4p=1$

$\Rightarrow p=1/4$