Question

Hi.

I would like to have a more detailed explanation to this problem... Thanks!

In a tennis match, a player must win three of five sets to win the match. If a player wins the first two sets, what is the probability that the player will win the match, assuming that each player is equally likely to win each set?

Answer 1

Total number of sets = 5

Minimum number of sets to win = 3

Given:

the player wins the first 2 matches.

Total number of sets remaining = 5 - 2 = 3

Munimum number sets to win = 3 - 2 = 1

p = q = 0.5

So,

the player will win the match if:

(i) He wins 1 of the remaining 3 matches and looses in 2 other matches:
Probability:

(ii) He wins 2 of the remaining 3 matches and looses in 1 other match.

Probability =

(iii) He wins all the remaining 3 matches.

Probability = 0.5³ = 0.125

So,

the required probability = 0.375 + 0.375 + 0.125 = 0.875

So,

the answer is:

0.875