Question

Let A and B be events with P(A)=0.7,P(B)=0.3, and P(BA)=0.2. Find P(A and B). 0.06 0.21 0.14 0.29

Answer 1

The probability of events A and B both occurring is 0.2.

Step-by-step explanation:

The question asks to find P(A and B), which represents the probability of events A and B both occurring. In this case, we are given that P(A) = 0.7, P(B) = 0.3, and P(B and A) = 0.2. To find P(A and B), we can use the formula P(A and B) = P(B|A) * P(A), where P(B|A) represents the probability of event B occurring given that event A has already occurred. We can calculate P(B|A) as P(B and A) / P(A), which gives us P(B|A) = 0.2 / 0.7 = 0.2857. Using this value and P(A) = 0.7, we can compute P(A and B) as P(A and B) = P(B|A) * P(A) = 0.2857 * 0.7 = 0.2.