Question

Given P(A) = 0.55, P(B) = 0.42 and P(AUB) = 0.639, find the value of

P(An B), rounding to the nearest thousandth, if necessary.

Answer 1

The probability of A and B, denoted as P(A ∩ B) is equal to 0.331.

Explanation:

Recall our formula for the probability of A or B:

• P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

We are given are variables already, which we can once again define:

• P(A) = 0.55
• P(B) = 0.42
• P(A ∪ B) = 0.639

To find P(A ∩ B), we start by plugging in the values into our formula:

• 0.639 = 0.55 + 0.42 - P(A ∩ B)

We can add the RHS of the equation:

• 0.639 = 0.97 - P(A ∩ B)

Subtracting 0.97 on both sides, we get closer to our answer:

• -0.331 = -P(A ∩ B)

To obtain our final answer, we can simply just divide both sides by -1:

• 0.331 = P(A ∩ B)
• P(A ∩ B) = 0.331

Therefore, the probability of A and B is equal to 0.331.