<p>Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is</p>
Step-by-Step Solution
Key Concept: Use complement approach: find probability that Mr. A selected at least one winning horse. When exactly one horse wins the race, Mr. A wins his bet if at least one of his two selected horses is the winner.
<p><strong>Step 1:</strong> Total ways to select 2 horses from 5: C(5,2) = 10</p><p><strong>Step 2:</strong> When the race happens, exactly 1 horse wins. For Mr. A to win his bet, the winning horse must be one of his 2 selected horses.</p><p><strong>Step 3:</strong> Number of ways to select 2 horses such that 1 specific winning horse is included: We need that winning horse + 1 more from remaining 4 = C(4,1) = 4</p><p><strong>Step 4:</strong> Probability = (Favorable outcomes)/(Total outcomes) = 4/10 = 2/5</p><p><strong>Alternative using complement:</strong> P(Mr. A selected winner) = 1 - P(Mr. A did NOT select winner) = 1 - C(4,2)/C(5,2) = 1 - 6/10 = 4/10 = 2/5</p><p>∴ Answer: C (2/5)</p>
Correct Answer: C