Question

Three friends (a, b, and

Answer 1

A) P(A beats b) = 0.7 P( A beats C) = 0.9 Also P(b beats c) = 0.3
 P (A wins both of her matches and b defeats c) = 0.7 * 0.9 * 0.3 = 0.189
 B) P( A wins both of her matches) = 0.7 * 0.9 = 0.63
 C) P( A loses against b) = 1 - 0.7 = 0.3 and against c = 1 - 0.9 = 0.1
 P (A loses against b and c) = 0.1 * 0.3 = 0.03
 D) Probability that A wins one match = (A beats B and B beats C and C beats A) + P(A beats C and C beats B and B beats A)
 P = (A beats B) * P(B beats C) * P(C beats A) + P(A beats C) * P(C beats B) * P(B beats A) = (0.7) * (0.3) * (0.1) + (0.9) * (0.7) * (0.3) = 0.021 + 0.189 = 0.21