What is the P(A and B) given that P(A) = 0.53, P(B) = 0.39, and P(A or B) = 0.48

Question

asked Feb 6, 2022 231k views

1 Answer

Ofer Herman · Answer 1 · 2022-02-11T02:28:43+0000

Answer:

P(A and B) = 0.44

Explanation:

Venn probabilities:

Suppose that we have two events, A and B. The probability of A and B is:

$P(A \cap B) = P(A) + P(B) - P(A \cup B)$

In which
$P(A \cup B)$ is P(A or B).

In this question:

$P(A) = 0.53, P(B) = 0.39, P(A \cup B) = 0.48$

Then

$P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.53 + 0.39 - 0.48 = 0.44$

So

P(A and B) = 0.44