Question

Let A denote the event that a person consumes Coca-Cola and B when they consume Pepsi.

Suppose P(A)=0.50 and P(B)=0.30.

a) Why is it not the case that P(A) + P(B) = 1?
b) Calculate P(B')
c) Calculate P(A ∩ B)
d) Calculate P(A ∪ B)

Answer 1

a. P(A) + P(B) does not equal 1 because events A and B are not mutually exclusive. b. P(B') = 1 - P(B) = 0.70. c. The probability of A and B happening simultaneously depends on their specific relationship. d. The exact value of P(A ∪ B) can't be determined without additional information.

Step-by-step explanation:

a. P(A) + P(B) does not equal 1 because events A and B are not mutually exclusive. There can be cases where a person consumes both Coca-Cola and Pepsi, hence the probability of their union (P(A ∪ B)) is greater than the sum of their individual probabilities (P(A) + P(B)).

b. P(B') = 1 - P(B) = 1 - 0.30 = 0.70.

c. P(A ∩ B) is the probability of both events A and B happening simultaneously.

Since A and B are different events, the probability of their intersection would depend on the specific information given about their relationship.

d. P(A ∪ B) is the probability of either event A or event B happening.

To calculate this, we can use the formula: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Given P(A) = 0.50, P(B) = 0.30, and no information about P(A ∩ B), we cannot determine the exact value of P(A ∪ B).