<p>A man and a woman appear in an interview for two vacancies in the same post. The probability of man's selection is 1/4 and that of the woman's selection is 1/3. What is the probability that none of them will be selected?</p>
Step-by-Step Solution
Key Concept: The selections of the man and woman are independent events. The probability that NONE are selected equals the product of their individual probabilities of NOT being selected.
<p><strong>Step 1:</strong> Identify the given probabilities.</p><p>P(Man selected) = 1/4, so P(Man NOT selected) = 1 - 1/4 = 3/4</p><p>P(Woman selected) = 1/3, so P(Woman NOT selected) = 1 - 1/3 = 2/3</p><p><strong>Step 2:</strong> Apply independence. Since the selections are independent events, the probability that BOTH are not selected is the product of their individual probabilities of not being selected.</p><p>P(None selected) = P(Man NOT selected) × P(Woman NOT selected)</p><p>P(None selected) = (3/4) × (2/3) = 6/12 = 1/2</p><p><strong>∴ Answer: 1/2</strong></p>
Correct Answer: 1/2