JEE Advanced2016MathematicsProbabilityActual
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
- A1 4
- B5 12
- C1 2
- D7 12
Correct answer
B. 5 12
Step-by-step solution
P X > Y = P T 1   w i n   P T 1 w i n + P T 1 w i n   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 = 1 2 × 1 2 + 1 2 × 1 6 + 1 6 × 1 2 = 5 12