# Let x be a discrete random variable. If pr(x less than 10) = 1/4, and pr(x greater than 10) =...

## Question:

Let {eq}x {/eq} be a discrete random variable. If {eq}pr(x < 10) = \frac{1}{4} {/eq}, and {eq}pr(x > 10) = \frac{1}{7} {/eq}, then what is {eq}pr(x = 10) {/eq}?

## Discrete random variable

A discrete random variable is known as discrete random because of the two reasons:-

i. Discrete because it assumes particular values like 0, 1, 2 and so on.

ii. Random because the total probability equals one.

We have to find P (X = 10)

P (X = 10) = P (X > 10) - P (X < 10)

{eq}P (X = 10) = \frac{1}{4}-\frac{1}{7} {/eq}

{eq}P (X = 10) = \frac{7-4}{28} {/eq}

{eq}P (X = 10) = \frac{3}{28} {/eq}

Hence, the P (X = 10) = 3/28.