<p>India and Pakistan is playing a best four of 7 match series. What is the probability that the tournament ends up in 6 matches assume that no match ends up in a draw?</p>
Step-by-Step Solution
Key Concept: For a best-of-7 series to end in exactly 6 matches, one team must win 4 matches with the 6th match being the decisive 4th win. This means after 5 matches, the score must be 3-2, and the team leading 3-2 must win match 6.
<p><strong>Step 1:</strong> For a best-of-7 series to end in exactly 6 matches, one team must achieve their 4th win on the 6th match.</p><p><strong>Step 2:</strong> This means after 5 matches, the score is 3-2 (one team has 3 wins, other has 2 wins).</p><p><strong>Step 3:</strong> In the first 5 matches, one specific team (say India) wins exactly 3 matches: C(5,3) = 10 ways, each with probability (1/2)^5.</p><p><strong>Step 4:</strong> India must win the 6th match (probability = 1/2).</p><p><strong>Step 5:</strong> Since either India OR Pakistan can be the team winning 3-2, multiply by 2.</p><p><strong>Step 6:</strong> P(series ends in 6) = 2 × C(5,3) × (1/2)^5 × (1/2) = 2 × 10 × (1/2)^6 = 20/64 = <strong>5/16</strong></p><p>∴ Answer: B</p>
Correct Answer: B