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

Question

6. A and B are professional tennis players. They play two matches against each other. Player A has a probability of winning match 1 of 0.6. Player A also has a probability of winning match 2 of 0.6. However, if player A wins the first match there is a 0.7 chance that player 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

a) let W reresent win and L represnet Lose ; therefore from above given information below is joint probability distribution for match 1 and match 2 outcome for player A:

b) probability that A wins At least 1 match =1-P( A loses both the matches =1-0.22 =0.78

c)probability that player A loses 2nd match given loses first match =P(L2|L1) =0.22/0.4 =0.55

as from above P( losing 1st match)*P( losing 2nd match)=0.4*0.4 =0.16 which is not equal to 0.22 ( P( losing 1st match and losing 2nd match))

also as P(L2|L1) is not equal to P(L2)  

therefore events are not independent,

match 2 match 1 W2 L2 total W1 0.42 0.18 0.6 L1 0.18 0.22 0.4 total 0.6 0.4 1

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