Three friends A B and C will participate in a roundrobin tou

Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose that

P(A beats B) = 0.6
P(A beats C) = 0.7
P(B beats C) = 0.5

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?


(c) What is the probability that A loses both her matches?


(d) What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.)

Solution

A) A WINNING BOTH THE MATCHES AND B WINING C CAN BE FOUND THE MULTIPLYING PROBABILITY OF ALL 3 = 0.6*0.7*0.5=0.210

B) PROBABILITY OF A WIINING BOTH IS 0.6*0.7 = 0.42 ( WHEN AND COMES IT MEANS MULTIPLY)

C)PROBABILITY OF A LOSING BOTH = 1 - PROBABILITY OF A WINING BOTH = 1-0.42 = 0.58

D)2 WAYS

1ST A BEAT B AND B BEAT C AND C BEAT A=0.6*0.5*0.3 =0.09

2ND B BEAT A AND A BEAT C AND C BEAT B= 0.4*0.7*0.5 = 0.14