Football teams `T_(1)` and `T_(2)` have to play two games against each other. It is assumed that the outcomes of the two games are independent. The pr

Question

Football teams T 1 T and T 2 T have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T 1 T winning,drawing and losing a game against T 2 T are 1 2 , 1 6 1 and 1 3 1 , respectively. Each teams gets 3 points for a win, 1 point of a drawn and 0 point for a loss in a games. P ( X > T ) P is A. 1 4 1 B. 5 12 5 C. 1 2 1 D. 7 12 7 Select the correct answer from above options

Answer 1

Correct Answer - B Consider the following events : W i j W =Team T i T wins in j t h j game D i = i t h D game is draw, i=1,2 P ( X > Y ) = P { ( W 11 ∩ W 12 ) ∪ ( W 11 ∩ D 2 ) ∪ ( D 1 ∩ W 12 ) } P = P ( W 11 ∩ W 12 ) + P ( W 11 ∩ D 2 ) + P ( D 1 ∩ W 12 ) = = P ( W 11 ) P ( W 12 ) + P ( W 11 ) P ( D 2 ) + P ( D 1 ) P ( W 12 ) = = 1 2 × 1 2 + 1 2 × 1 6 + 1 6 × 1 2 = 5 12 =