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Paragraph: 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 1 2 , 1 6 and 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, a

Options

  1. A11 36
  2. B1 3
  3. C13 36
  4. D1 2

Correct answer

C. 13 36

Step-by-step solution

P X = Y = P m a t c h   d r a w P m a t c h   D r a w + P T 1 w i n   P T 2 w i n + P T 2 w i n   P T 1 w i n = 1 6 × 1 6 + 1 2 × 1 3 + 1 3 × 1 2 = 13 36

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