Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Probability

Question:

If in a binomial distribution n = 4, P(X = 0) = $\frac{16}{81}$, then P(X = 4) equals:

Options:

$\frac{1}{16}$

$\frac{1}{81}$

$\frac{1}{27}$

$\frac{1}{8}$

Correct Answer:

$\frac{1}{81}$

Explanation:

The correct answer is Option (2) - $\frac{1}{81}$

$P(X = 0) = \frac{16}{81}$

so ${^4C}_0×P^0(1-P)^4=\frac{16}{81}$

$1-P=\frac{2}{3}⇒P=\frac{1}{3}$

$P(X = 4) ={^4C}_4P^4(1-P)^0=\frac{1}{81}$