If X B(4, p) and P(X=0)=16 81 , then P(X=4)= - Vidyadip

MCQ

If $X \sim B(4, p)$ and $P(X=0)=\frac{16}{81}$, then $P(X=4)=$

A
$\frac{1}{16}$
✓
$\frac{1}{81}$
C
$\frac{1}{27}$
D
$\frac{1}{8}$

✓

Answer

Correct option: B.

$\frac{1}{81}$

(b) $\frac{1}{81}$
$\text { Hint }: P(X=0)={ }^4 C_0 P^0 q^4=\frac{16}{81} $
$\therefore q^4=\left(\frac{2}{3}\right)^4 \quad \therefore q=\frac{2}{3} $
$\therefore p=1-q=1-\frac{2}{3}=\frac{1}{3}$
$\therefore P(X=4)={ }^4 C_4 p^4 q^0=\left(\frac{1}{3}\right)^4=\frac{1}{81}$.

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