Question

Which of the following statements is true for two events, each with a probability greater than 0?

1) The probability of both events occurring is always 1.
2) The probability of either event occurring is always 1.
3) The probability of both events occurring is always less than 1.
4) The probability of either event occurring is always less than 1.

Answer 1

The true statement for two events with probabilities greater than 0 is that the probability of both events occurring is always less than 1.

Step-by-step explanation:

The statement that is true for two events, each with a probability greater than 0, is 3) The probability of both events occurring is always less than 1. If the events are independent, the probability of A and B occurring together, denoted as P(A AND B), is given by the multiplication rule, which is P(A) × P(B). If P(A) > 0 and P(B) > 0, then P(A AND B) will also be greater than 0, but certainly less than 1. If the events are dependent, the same logic applies but you would use conditional probabilities. Similarly, the probability of either event A or event B occurring, P(A OR B), is given by the addition rule: P(A) + P(B) − P(A AND B), which will also be less than 1, because P(A) and P(B) are each less than 1, and subtracting P(A AND B) reduces the total probability further.