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November 16th, 2008, 01:02 AM   #1
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Another probability problem

In a tennis game once the score has reached "deuce"play continues until one player has a lead of 2 points

Mike and Bob are playng tennis and the score reached deuce.Suppose each point is won by Mike with probability 1/4(and otherwise by Bob)and the outcome of each point is independent of all other points.

If "x" is the probability that Mike wins,"u" is the conditionl probability that Mike wins given that he wins the first point and "v" the conditional probability Mike wins given that he loses the first point
How do i use the theorem of total probability to show that

4x=u+3v
4u=3x+1
4v=x

how can i find the probability that Mike wins the match?
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