Question

Find the indicated probability. For a person selected randomly from a certain population, events A and B are defined as follows:

Event A: The person is male
Event B: The person is a smoker

For this particular population, it is found that P(A)=0.52, P(B)=0.26, P(A∩B)=0.14. Find P(A∪B). Round approximations to two decimal places.

a) 0.64
b) 0.74
c) 0.38
d) 0.92

Answer 1

The probability of a person being either male or a smoker or both in the given population is 0.64. This is found by using the formula for the union of two events, which is P(A UNION B) = P(A) + P(B) - P(A INTERSECT B).

Step-by-step explanation:

To find the probability of the union of the events A and B, P(A∪B), we use the formula:

P(A∪B) = P(A) + P(B) − P(A∩B)

Substitute the given probabilities into the formula:

P(A∪B) = 0.52 + 0.26 − 0.14

This simplifies to:

P(A∪B) = 0.64

Therefore, the indicated probability of a person being either male or a smoker or both in this particular population is 0.64.