The odds in favour of A winning a game of table tennis against B are 1:2. If 3 games are to be played, then the probability of A winning at least two games out of the three is.....

Step-by-step solution

Given odds in favour of A winning are 1:2 . Probability of A winning a game is p = 1 1+2 = 1 3 . Probability of A losing a game is q = 1 - p = 2 3 . Total number of games played is n = 3 . Probability of A winning at least two games is P(X 2) = P(X = 2) + P(X = 3) . Using binomial distribution, P(X = r) = ^ n C_ r p^ r q^ n-r . P(X 2) = ³C₂ ( 1 3 )² ( 2 3 )¹ + ³C₃ ( 1 3 )³ ( 2 3 )⁰ P(X 2) = 3 1 9 2 3 + 1 1 27 1 P(X 2) = 6 27 + 1 27 = 7 27 Answer: 7 27