Question

Have Retirement Benefits

Answer 1

Answer:

(a) The probability of the intersection of events "man" and "yes" is 0.55.

(b) The probability of the intersection of events "no" and "man" is 0.10.

(c) The probability of the union of events "woman" or "no" is 0.45.

Step-by-step explanation:

The information provided is:

             Yes    No   Total

Men       275   50     325

Women  150   25      175

Total      425   75      500

(a)

Compute the probability that a randomly selected employee is a man and a has retirement benefits as follows:

$P(M\cap Y)=\frac{n(M\cap Y)}{N}=\frac{275}{500}=0.55$

Thus, the probability of the intersection of events "man" and "yes" is 0.55.

(b)

Compute the probability that a randomly selected employee does not have retirement benefits and is a man as follows:

$P(N\cap M)=\frac{n(N\cap M)}{N}=\frac{50}{500}=0.10$

Thus, the probability of the intersection of events "no" and "man" is 0.10.

(c)

Compute the probability that a randomly selected employee is a woman or has no retirement benefits as follows:

$P(W\cup N)=P(W)+P(N)-P(W\cap N)=\frac{175}{500}+\frac{75}{500}-\frac{25}{500}=0.45$

Thus, the probability of the union of events "woman" or "no" is 0.45.