Probability
Independent Events
Grade 12
Question:
<p>Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T1 winning, drawing and losing a game against T2 are \(\frac{1}{2}\), \(\frac{1}{6}\) and \(\frac{1}{3}\) respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T1 and T2 respectively, after two games. Find \(P(X = Y)\).</p>
<p>(a) \(\frac{11}{36}\)</p>
<p>(b) \(\frac{1}{3}\)</p>
<p>(c) \(\frac{13}{36}\)</p>
<p>(d) \(\frac{1}{2}\)</p>
Step-by-Step Solution
Key Concept: Identify all scenarios where X = Y after two games and sum their probabilities.
<p>This is a passage-based question requiring analysis of match outcomes and point calculations where both teams score equal points.</p>
Correct Answer: C