Question

[ P(A) = 0.60, quad P(B) = 0.20, quad P(A cap B) = 0.15 ]

What is ( P(A cup B) )?
a. 0.80
b. 0.40
c. 0.65
d. 0.12

Answer 1

To find P(A ∪ B), apply the principle of inclusion-exclusion. Given P(A), P(B), and P(A ∩ B), calculate P(A ∪ B) = P(A) + P(B) - P(A ∩ B), which equals 0.65.

Step-by-step explanation:

The question is about finding the probability of either event A or event B occurring, which is denoted as P(A ∪ B). This can be found by applying the principle of inclusion-exclusion for probabilities:

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

Given that:

We can substitute these values into the formula:

P(A ∪ B) = 0.60 + 0.20 − 0.15

P(A ∪ B) = 0.80 − 0.15

P(A ∪ B) = 0.65

So, the correct answer is c. 0.65.