Prob (1 Viewer)

[Vampire]

Hey everyone, I'm having a little trouble with this question so any help would be appreciated...

A tennis match between two players consist of a number of sets. The match continues until one of the players has won 3 sets.
Whenever Pat and John play, on average, for each set they play, there is a probability of 2/3 that Pat wins and a probability of 1/3 that John wins.

Find Probability that Pat wins match (4 marks)

Thx

 

[Ogden_Nash]

I'll give it a shot....(no pun intended )

P(Pat winning) = P(win in 3 sets) + P(win in 4 sets) + P(win in 5 sets)
........................= (2/3)³ + (2/3)*³C₁*(2/3)²*(1/3) + (2/3)*⁴C₂*(2/3)²*(1/3)²
........................= 64/81

[Note: for a 4 or 5 setter, the final set must be won by Pat, so only the remaining sets may be ordered differently.]

Hope that helps.
Someone please correct me if I've made a mistake...

 

[shafqat]

It has to finish in 5 sets, as by then someone will have one 3 of them.

 

[Vampire]

my bad...lol

thx