Question

Let A and B be two events. Suppose that P(A) = 0.4, P(B) = 0.5,

and P(A ∩ B) = 0.1. Find the probability that A or B occurs, but
not both.

Answer 1

To find the probability that A or B occurs, but not both, use the formula P(A OR B) = P(A) + P(B) - 2 * P(A ∩ B). Substitute the given values into the formula to calculate the probability.

Step-by-step explanation:

To find the probability that A or B occurs, but not both, we can use the formula P(A OR B) = P(A) + P(B) - 2 * P(A ∩ B).

Given that P(A) = 0.4, P(B) = 0.5, and P(A ∩ B) = 0.1, we can substitute these values into the formula to calculate:

P(A OR B) = 0.4 + 0.5 - 2 * 0.1 = 0.4 + 0.5 - 0.2 = 0.7 - 0.2 = 0.5

Therefore, the probability that A or B occurs, but not both, is 0.5.