Final answer:
To calculate the union of two events A and B, apply the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B). For P(A) = 0.5, P(B) = 0.3, and P(A ∩ B) = 0.15, it results in P(A ∪ B) = 0.65. Subsequently, the complement, P(A ∪ B)', is 1 - P(A ∪ B) = 0.35, which is not listed in the given options.
Step-by-step explanation:
To find the probability of the union of two events, A and B, we use the formula:
P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
Given that P(A) = 0.5, P(B) = 0.3, and P(A ∩ B) = 0.15, we substitute these values into the formula:
P(A ∪ B) = 0.5 + 0.3 − 0.15 = 0.65
The probability of the complement of A union B, denoted as P(A ∪ B)', is found by subtracting P(A ∪ B) from 1. So:
P(A ∪ B)' = 1 − P(A ∪ B) = 1 − 0.65 = 0.35
However, since none of the options given matches this result, there may have been a typo in the question or with the options provided. If the question and options were provided exactly as shown, it suggests that there is no correct answer listed. Otherwise, the correct calculation given the probabilities provided would be 0.35, not found in options a) 0.80, b) 0.20, c) 0.65, or d) 0.18.