What logical conclusion can be drawn if P(A) + P(A') = 1?

What logical conclusion can be drawn if P(A) + P(A') = 1?

• A. Both events cannot happen
• B. At least one event must happen
• C. Both events can happen simultaneously
• D. P(A) and P(A') are independent

Answer: (B)

When we have the equation P(A) + P(A') = 1, it signifies a fundamental principle in probability regarding complementary events. Here, P(A) is the probability of event A occurring, while P(A') represents the probability of event A not occurring. Since the sum of these two probabilities equals 1, it can be concluded that if one event happens, the other must not happen, and vice versa. This relationship means that between the two events A and its complement A', at least one of them must occur in any given scenario. This conclusion aligns with the definition of complementary probabilities—either event A happens, or event A does not happen, covering all possible outcomes. Consequently, the correct conclusion drawn from the equation is that at least one of the events must happen.

When we have the equation P(A) + P(A') = 1, it signifies a fundamental principle in probability regarding complementary events. Here, P(A) is the probability of event A occurring, while P(A') represents the probability of event A not occurring.

Since the sum of these two probabilities equals 1, it can be concluded that if one event happens, the other must not happen, and vice versa. This relationship means that between the two events A and its complement A', at least one of them must occur in any given scenario.

This conclusion aligns with the definition of complementary probabilities—either event A happens, or event A does not happen, covering all possible outcomes. Consequently, the correct conclusion drawn from the equation is that at least one of the events must happen.