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

Question

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

Let A1 shows the event that player A win the match 1and let A2 shows the event that player A win the match2. So we have

P(A1) = 0.6, P(A2) = 0.6, P(A2|A1) = 0.7

Let B1 shows the event that player A loose the match 1 and let B2 shows the event that player A losse the match2. So we have

P(B1) = 1-P(A1) = 0.4

P(B2)= 1-P(A2) = 0.4

P(B2|A1) = 1- P(A2|A1) = 0.3

Now,

P(A2 and A1) = P(A2|A1)P(A1) = 0.7 * 0.6 = 0.42

P(B2 and A1) = P(B2|A1)P(A1) = 0.3 *0.6 = 0.18

Following is the joint probability table:

b)

P(A1 or A2) = P(A1)+P(A2)-P(A1 and A2) = 0.6+0.6 - 0.42 = 0.78

c)

The required probability is

P(B2|B1) = P(B2 and B1) / P(B1) = 0.22 / 0.4 = 0.55

No the events “player A losing the first match” and “player A losing the second match” are not independent since P(B2|B1) is not equal to P(B2).

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