Question

Find the probabilities of the events below. Write each answer as a single fraction P(A) =P(B) =P(A or B) = P(A and B) =P(A) + P(B) - P(A and B) =Select the prob. that is equal to P(A) + P(B) - P(A and B) =1. P(A) 2. P(B) 3. P(A or B) 4. P(A and B) ​

Answer 1

In probability theory, P(A OR B) represents the probability that either event A, B, or both occur. The correct expression for P(A OR B) is P(A) + P(B) - P(A AND B), and thus the answer to which option equals P(A) + P(B) - P(A AND B) is option 3: P(A OR B).

Step-by-step explanation:

The question asks for finding the probabilities of different combinations of two events: A and B. The probabilities are written as P(A), P(B), P(A OR B), and P(A AND B), with P(A OR B) being the probability that either A, B, or both occur, and P(A AND B) being the probability that both A and B occur simultaneously.

By applying the addition rule of probabilities, which states that the probability of A or B is given by P(A OR B) = P(A) + P(B) − P(A AND B), we can find the individual probabilities. Given two events A and B, we can see that option 3, P(A OR B), corresponds to P(A) + P(B) − P(A AND B), which is the formula to calculate the probability of either A or B happening.

It's important to remember that if A and B are mutually exclusive, then P(A AND B) = 0, resulting in P(A OR B) = P(A) + P(B). However, if they are not mutually exclusive, the intersection of A and B needs to be subtracted to avoid double-counting the probability where both A and B occur.