An event X can happen with probability p and event Y can happen with probability q. Further, X and Y are independent events. Which of the following statements is/are correct?<br>I. The probability that <strong>EXACTLY</strong> one of the events happens is p+q-pq.<br>II. The probability that <strong>AT LEAST</strong> one of the events happens is p+q-2pq.<br>Select the answer using the code given below.
- A. I only
- B. II only
- C. Both I and II
- D. Neither I nor II ✓
Correct Answer: D. Neither I nor II
Explanation
The correct formulas are interchanged in the statements. The probability that exactly one of the events happens is P(X) + P(Y) - 2P(X \cap Y) = p+q-2pq. The probability that at least one of the events happens is P(X \cup Y) = P(X) + P(Y) - P(X \cap Y) = p+q-pq. Thus, both statements are incorrect.
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