Question

A random variable X has the following probability distribution

X	0	1	2	3	4
P(X)	k	2k	4k	2k	k

then the value of P(1 ≤ X < 4 | X ≤ 2) =

Options

• \[\frac{5}{6}\]

• \[\frac{6}{7}\]

• \[\frac{7}{8}\]

• \[\frac{8}{9}\]

Answer 1

\[\frac{6}{7}\]

Explanation:

P(1 ≤ X < 4 | X ≤ 2)

\[=\frac{\mathrm{P}\left(1\leq\mathrm{X}<4\cap\mathrm{X}\leq2\right)}{\mathrm{P}\left(\mathrm{X}\leq2\right)}\]

\[=\frac{\mathrm{P}\left(1\leq\mathrm{X}\leq2\right)}{\mathrm{P}\left(\mathrm{X}=2\right)}\]

\[=\frac{\mathrm{P}\left(\mathrm{X}=1\right)+\mathrm{P}\left(\mathrm{X}=2\right)}{\mathrm{P}\left(\mathrm{X}=0\right)+\mathrm{P}\left(\mathrm{X}=1\right)+\mathrm{P}\left(\mathrm{X}=2\right)}\]

\[=\frac{6\mathrm{k}}{7\mathrm{k}}=\frac{6}{7}\]