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)?

P(x=5) = 7/12

Step-by-step 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.

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