Question

In tennis, if two players are tied 3-3 after six points, they continue to play until one player is ahead of the other by two points; that player then wins the game. Suppose that Nathan and Carl are playing tennis, and that Nathan will win a point over Carl on average 2/3 of the time. If they're tied at 3-3. what is the probability that Nathan will win? Choose the best answer. (4)- () -1 ()' ()- ()

Answer 1

After 2 rounds, either Nathan has won or Carl has won or they are back to a tied situation.

So Nathan wins if and only if we wins in the first two rounds, or if the first two rounds lead to a tie situation and Nathan wins in the fourth round, or if these two rounds also lead to a tie situation and Nathan wins in the 6th round etc

A tie situation has probability

2 4 2 xxx 3 3 COIN

Required probability of Nathan winning is

2 2 P + + N

Which is an geometric series with

2 a= 3 9

Required probability is

P = 1 r 2 1

Checking the only answer matching is (both equal to 0.8)

2 2 4 - 1 ()-1

Correct option is the first one

2 2 4 - 1 ()-1

$\blacksquare$

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