5. A and B are professional tennis players. They play two matches against each o

Question

5. A and B are professional tennis players. They play two matches against
each other. Player A and player B each has a 0.5 chance of winning eachmatch. However, if player A wins the first match there is a 0.6 chance thatplayer A will win the second match.

a) Construct an appropriate joint probability table for this question.

b) What is the probability that player A wins at least one match?

c) What is the probability that player A loses the 2nd match given that player A lost the 1st match? Are the events “player A losing the first match” and“player A losing the second match” independent?

Explanation / Answer

Player B

(losing)

Player A

(winning)

b)

P(A wins atleast one match)=P(A wins 1st match only)+P(A wins 2nd match only)+P(A wins both the matches)

P(A wins 1st match only)=P(A wins 1st)P(A looses 2nd)=0.5*0.4=0.2

P(A wins 2nd match only)=P(A looses 1st)P(A wins 2nd)=0.5*0.4=0.2

P(A wins both the matches)=P(A wins 2nd match/A wins1st match)P(A wins 1st)=0.6*0.5=.3

P(A wins atleast one match)=0.7

P(A loses 2nd/A lost 1st)=1-P(A wins 2nd/A lost 1st)=1-.5=0.5

P(A losing 1st match)P(A losing 2nd match)=0.5*{P(A losing 2nd match/A losing 1st match)+P(A losing 2nd match/A winning 1st match)}

= 0.5{0.5+0.4}=0.45

So both are not independent of each other.

Player B

(losing)

Player A

(winning)

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