Three friends (A, B, and C) will participate in a round-robin tounament in which

Question

Three friends (A, B, and C) will participate in a round-robin tounament in which each one plays both of the others. Suppose that P(A beats B)0.4 PIA beats C)-0. P(B beats C)-0. and that the outcomes of the three matches are independent of one another (a) What is the probability that A wins both her matches and that B beats C b) What is the probability that A wins both her matches? ) What is the probability that A loses both her matches? that each person wins one match? (Hint: There are two different ways for this to happen) Need Help? oTaTr

Explanation / Answer

a)P(A wins both matches and B beats C)=0.4*0.6*0.8=0.192

b)

P(A wins both matches)=0.4*0.6=0.24

c)

P(A loses both)=(1-0.4)*(1-0.6)=0.24

d)

P(each person wins one)=P(A wins from B and B wins from C and C wins from A)+P(A wins from C and B wins from A ; C wins from B)=0.4*0.8*0.4+0.6*0.2*0.6=0.20

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