Question

Let E be the event that a randomly chosen person exercises. Let D be the event that a randomly chosen person is on a diet. Identify the answer which expresses the following with correct notation: Of all the people who exercise, the probability that a randomly chosen person is on a diet.

a) P(D) AND P(E)
b) P(E AND D)
c) P(E|D)
d) P(D|E)

Answer 1

d) P(D|E)

Explanation:

E = person exercises

D = person on a diet

Given the expression :

Of all the people who exercise, the probability that a randomly chosen person is on a diet.

This simply refers to a conditional probability whereby the subset from which the probability that a randomly chosen person is on diet is to be calculated is the subset of those who exercise.

In statistical parlance, the statement is expressed as ; the probability of A given B = P(A|B)

In this scenario, we say; the probability that a randomly chosen person is on a diet Given that the person exercise ; P(D|E)

Hence, the answer is D.