Question

A random variable $X$ has the following probability distribution : x	0	1	2	3	4
P(x)	k	2k	4k	6k	8k

The value of $P(1 < X < 4 | x ≤ 2)$ is equal to

• A. $\frac{4}{7}$
• B. $\frac{2}{3}$
• C. $\frac{3}{7}$
• D. $\frac{4}{5}$

Answer 1

Answer: (A)

$\frac{4}{7}$

Answer 2

$∵ \;x$ is a random variable

$∴\; k + 2k + 4k + 6k + 8k = 1$

$∴\; k =\frac{1}{21}$

Then, $P(1<x<4)|x<=2)$

=$\frac{4k}{7k}$

= $\frac{4}{7}$

Hence, the correct option is (A): $\frac{4}{7}$