Question

The probability of a randomly selected employee of a company being male is 60%. The probability of the employee being less than 30 years old is 70%. If the probability of the employee being less than 30 years old given that the employee is a male is 40%, what is the probability that the employee is a male, given that the employee is less than 30 years old? A. 0. 34 B. 0. 42 C. 0. 55 D. 0. 69 E. 0. 71.

Answer 1

The probability that the employee is a male, given that the employee is less than 30 years old is given by: Option A: 0.3 (approx)

What is chain rule in probability?

For two events A and B, by chain rule, we have:

$P(A \cap B) = P(B)P(A|B) = P(A)P(B|A)$

where P(A|B) is probability of occurrence of A given that B already occurred, ( and vice versa for P(B|A) )

For the given case, naming the events as:

A = Randomly selected employee being a male

B = Randomly selected employee being less than 30 years old

Then, by the specified data, we've got:

• P(A) = 60% = 0.6
• P(B) = 70% = 0.7
• P(B|A) = 40% = 0.4
• P(A|B) = ? (The needed quantity).

By using the chain rule, we get:

$P(B)P(A|B) = P(A)P(B|A)$

Thus, the value of P(A|B) is:

$P(B)P(A|B) = P(A)P(B|A)\\\\P(A|B) = \dfrac{P(A)P(B|A)}{P(B)} = \dfrac{0.6 \times 0.4}{0.7} \approx 0.34$

Thus, the probability that the employee is a male, given that the employee is less than 30 years old is given by: Option A: 0.3 (approx)

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