Question

Two events, A and B, are independent of each other. IfP(A)=0.6and P(B) 0.35, What is

P(AuB)?
A) 0.21
B) 0.6
C) 0.35
D) 0.74

Answer 1

To calculate the probability of the union of two independent events A and B, we use P(AuB) = P(A) + P(B) - P(A)P(B). With P(A) = 0.6 and P(B) = 0.35, the calculation yields P(AuB) = 0.74.

Step-by-step explanation:

The question is asking to calculate the probability of the union of two independent events, event A and event B. To find the probability of A union B, denoted as P(AuB), we use the formula:

P(AuB) = P(A) + P(B) - P(A AND B)

Since A and B are independent, the probability of A AND B is the product of their individual probabilities, P(A AND B) = P(A)P(B). Thus, we have:

P(AuB) = P(A) + P(B) - P(A)P(B)

Substituting the values given, P(A) = 0.6 and P(B) = 0.35:

P(AuB) = 0.6 + 0.35 - (0.6)(0.35)

P(AuB) = 0.6 + 0.35 - 0.21

P(AuB) = 0.95 - 0.21

P(AuB) = 0.74

Therefore, the correct answer is D) 0.74.