Question

Let X be a discrete random variable. If Pr(X<5) = 1/4, and Pr(X>5) = 1/6, then what is Pr(X=5)?

Answer 1

P(x=5) = 7/12

Explanation:

We find the probability of any number by subtracting or adding the other probabilities that are given. This we have to decide on our own what the situation is , whether to add or subtract depending on the probability given.

In this question we are given two probabilities which both are either less or greater than the P (x=5) so we subtract them from the probability of 1. As the total of all probabilities is equal to 1.

P(x=5) =1- P(x<5) - P (x> 5)

P(x=5) =1- 1/4-1/6

P(x=5) =24-6-4/24= 14/24= 7/12

Check the probabilities of all must equal 1

P(x=5) + P(x<5) + P (x> 5)

=7/12+ 1/4+1/6

=7+3+2/12= 12/12=1 which is true.

The diagram will help- you understand better.

Answer 2

The value is
`Pr(X = 5) = 0.5833`

Explanation:

From the question we are told that

The value of
`Pr(X < 5) = (1)/(4)`

The value of
`Pr(X > 5) = (1)/(6)`

Generally the total probability of X should be equal to 1

So

`Pr(X > 5) +Pr(X < 5)+ Pr(X = 5) = 1`

=>
`x^(2) (1)/(6) +(1)/(4) + Pr(X = 5) = 1`

=>
`Pr(X = 5) = 0.5833`