Question

10. If \( P(A)=0.35, P(B)=0.74 \), and \( P(A \cap B)=0.37 \); then \( P(A \cup B)= \) A. \( 1.21 \) B. \( 0.94 \) C. \( 0.72 \) D. \( 1.48 \) II. Problem Solving 1. A national survey indicated that \

Answer 1

The probability of the union of events A and B (P(A∪B)) is found by adding the individual probabilities of A and B and then subtracting the probability of their intersection. In this case,

P(A∪B)=0.35+0.74−0.37=0.72, which corresponds to option C.

This correct answer is C.

Step-by-step explanation:

To find P(A∪B), which represents the probability of the union of events A and B, you can use the inclusion-exclusion principle. This principle states that:

P(A∪B)=P(A)+P(B)−P(A∩B)

Here:

P(A) is the probability of event A (given as 0.35).

P(B) is the probability of event B (given as 0.74).

P(A∩B) is the probability of the intersection of events A and B (given as 0.37).

Now substitute these values into the formula:

P(A∪B)=0.35+0.74−0.37

Combine the terms:

P(A∪B)=0.72

So, the detailed explanation shows that the probability of the union of events A and B is 0.72, corresponding to option C.

This correct answer is C.