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Sagot :
Answer:
0.27 ; 0.30 ; 0.20 ; 0.21
Step-by-step explanation:
Given that :
P(A beats B) = 0.5
P(A beats C) = 0.6
P(B beats C) = 0.9
Since the outcomes are independent :
A.) probability that A wins both her matches and that B beats C
P(A beats B) * P(A beats C) * P(B beats C)
0.5 * 0.6 * 0.9 = 0.27
B.) probability that A wins both her matches
P(A beats B) * P(A beats C)
0.5 * 0.6 = 0.3
C.) probability that A loses both her matches?
(1 - P(A beats B)) * (1 - P(A beats C)
(1 - 0.5) * (1 - 0.6)
0.5 * 0.4 = 0.20
D.) probability that each person wins one match
Either (A beats B), (B beats C). (C beats A) OR (A beats C), (C beats B), (B beats A)
Hence;
(0.5 * 0.9 * (1 - 0.6)) + (0.6 * (1 - 0.9) * (1 - 0.5)) = 0.21
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