Question

Given P(A) = 0.25, P(B) = 0.64, and P(A and B) = 0.22, find the value of P(A or B), rounding to the nearest thousandth if necessary.

Answer 1

Using the inclusion-exclusion principle, the probability of either event A or event B occurring, P(A or B), is calculated as 0.67 by summing P(A) and P(B) and then subtracting P(A and B).

Step-by-step explanation:

The student wants to find the value of P(A or B), which is the probability of either event A or event B occurring. To calculate this, we can use the inclusion-exclusion principle:

P(A or B) = P(A) + P(B) − P(A and B)

Substituting the given probabilities into the formula, we get:

P(A or B) = 0.25 + 0.64 − 0.22

P(A or B) = 0.89 − 0.22

P(A or B) = 0.67

So the probability that event A or event B occurs is 0.67, rounded to the nearest thousandth if necessary.