Question
A certain team wins with probability 0.7, losses with probability 0.2 and ties with probability 0.1. The team plays three games. Find the probability that the team wins at least two of the games, but not lose.
Solution
Let W , L and T denote the events that the team wins, loses and ties respectively.
∴ P (W) = 0.7, P (L) = 0.2, P (T) = 0.1
Required probability = P (team wins at least two games but not loses)
= P (WWT) + P (WTW) + P (TWW) + P (WWW)
= P (W) P (W) P (T) + P (W) P (T) P (W) + P (T) P (W) P (W) + P(W) P(W) P(W)
= 3 [P (W) P (W) P (T)] + P (W) P (W) P (W)
= 3 [(0.7) (0.7) (0.1) + (0.7) (0.7) (0.7)
= 3 × 0.049 + 0.343 = 0.147 + 0.343
= 0.49
