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Q.

A and B play a game of tennis. The situation of the game is as follows; if one scores two consecutive points after a deuce he wins; if loss of a point is followed by win of a point, it is deuce. The chance of a server to win a point is 2/3. The game is at deuce and A is serving. Probability that A will win the match is, (serves are changed after each point scored) 

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a

2/5 

b

3/5 

c

1/2

d

4/5

answer is C.

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Detailed Solution

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Let assume that ‘A’ wins after n deuces,  n[(0,)]
Probability of a deuce  =23.23+13.13=59
(A wins his serve then B wins his serve or A loses his serve then B also loses his serve) 
Now
probability of 'A' winning the game
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