Question

Consider two events, A and B. Suppose that P(A)=.40,P(B)=.50, and P(A∩B)=0.2 . Calculate the value of P(A′∪B′)

Answer 1

To calculate P(A'∪B'), find the complements of A and B, then use the formula P(A'∪B') = P(A') + P(B') - P(A'∩B').

Step-by-step explanation:

To calculate the value of P(A'∪B'), we need to find the probability of the union of the complements of A and B.

The complement of event A (A') is the probability of A not happening, which is 1 - P(A). So, P(A') = 1 - 0.40 = 0.60.

The complement of event B (B') is the probability of B not happening, which is 1 - P(B). So, P(B') = 1 - 0.50 = 0.50.

To find the probability of the union of A' and B' (A'∪B'), we can use the formula P(A'∪B') = P(A') + P(B') - P(A'∩B'). Since A and B are independent events, P(A'∩B') = P(A') * P(B') = 0.60 * 0.50 = 0.30.

Therefore, P(A'∪B') = 0.60 + 0.50 - 0.30 = 0.80.