Discussion Forum

The mean and variance of a random variable X having binomial distribution are 4 and 2 respectively the P(x=1) is

Answer:

Explanation:

Given, $P(\overline{A\cup B}) =\frac{1}{6}$

$\Rightarrow P({A\cup B}) =1-\frac{1}{6}=\frac{5}{6}$

$P(\overline{A}) =\frac{1}{4}$ $\Rightarrow P(A) =1-\frac{1}{4}=\frac{3}{4}$

We know,

$P(A\cup B) = P(A) + P(B) - P(A \cap B)$

$\Rightarrow \frac{5}{6}=\frac{3}{4}+P(B)-\frac{1}{4}$

$\Rightarrow P(B)=\frac{1}{3}$

 P(A)≠P(B) so they are not equally likely

Also P(A) x P(B)=3/4 × 1/3= 1/4 = $P(A \cap B)$

So A & B are independent