Graduate Management Admission Test (GMAT) Practice Test

If the probability of A is p and the probability of B is q, how can the probability of one of A or B occurring be expressed?

1. p + q

2. p(1-q) + q(1-p)

3. p + q - pq

4. p(1+q)

The correct answer is: p(1-q) + q(1-p)

The probability of either event A or event B occurring can be defined using the principle of inclusion-exclusion in probability theory. When you want to find the probability of at least one of two events happening, you are essentially looking for the total of the probabilities of each event occurring minus the probability of both events occurring simultaneously. The correct approach to calculate the probability of either A or B is: 1. Start with the probability of A occurring, which is p. 2. Then add the probability of B occurring, which is q. 3. However, if both A and B occur simultaneously, you would have counted that outcome twice (once in p and once in q). Therefore, you must subtract the probability of both A and B happening at the same time, which is the product of their probabilities if A and B are independent: pq. This leads to the following formula for the probability of A or B occurring: P(A or B) = P(A) + P(B) - P(A and B) = p + q - pq. This result corresponds perfectly with the choice that expresses this thought correctly. The addition of p and q accounts for the individual probabilities of A and B, while the subtraction of pq adjusts for the overlap. The selected choice