Problem 3) A, B, and C are evenly matched tennis players. Initially A and B play a set and the winner then plays C. This continues, with the winner always playing the waiting player, until one of the players has won two sets in a row. That player is then declared the overall winner. Find the probability that A is the overall winner.

the probability that A is the overall winner is 5/14 or 0.35714

Step-by-step explanation:

Given the data in the question;

probability that A is the overall winner P[A is the overall winner]

⇒ + +  + ................

= + + + ........

P(A) = = =             ∴{ they are evenly matched player}

so P(A is overall winner) will be;

= ()² + ()⁵ + ()⁸ + ..........+ ()⁴ + ()⁷ + ()¹⁰ + .............

= ()² [1 + ()³ + ()⁶ + .........] + ()⁴[1 + ()³ + ()⁶ + .........]

= [ ()² + ()⁴ ] [ 1 / 1 - ()³ ]

= [ () + () ] [ ]

= ×

= 5/14 or 0.35714

Therefore, the probability that A is the overall winner is 5/14 or 0.35714

false

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