<p>The probability that Krishna will be alive 10 years hence is 7/15 and that Hari will be alive is 7/10. What is the probability that both Krishna and Hari will be dead 10 years hence?</p>
Step-by-Step Solution
Key Concept: Both being dead means neither survives, which requires finding P(not Krishna alive AND not Hari alive). Use complement rule: P(dead) = 1 - P(alive), then multiply independent probabilities.
<p><strong>Step 1:</strong> Find probability Krishna will be dead in 10 years.</p><p>P(Krishna dead) = 1 - P(Krishna alive) = 1 - 7/15 = 8/15</p><p><strong>Step 2:</strong> Find probability Hari will be dead in 10 years.</p><p>P(Hari dead) = 1 - P(Hari alive) = 1 - 7/10 = 3/10</p><p><strong>Step 3:</strong> Since the events are independent, multiply the probabilities.</p><p>P(both dead) = P(Krishna dead) × P(Hari dead) = (8/15) × (3/10) = 24/150 = 4/25</p><p><strong>Note:</strong> 4/25 = 8/50 (equivalent form)</p><p>∴ Answer: 8/50</p>
Correct Answer: 8/50