# Tennis probability

• Apr 14th 2009, 04:10 PM
Allenge
Tennis probability
I got a question about probability.....
The probability that a tennis set will go to a tiebreaker is 14%. In 80 randomly selected tennis sets, what is the mean and std dev. of the number of tie breakers?
a) mean: 10.4; std dev: 3.1
b) mean: 10.4; std dev: 3.35
c) mean: 11.2; std dev: 3.10
d) mean: 11.2; std dev 3.35

Thanks everybody
• Apr 14th 2009, 06:44 PM
nzmathman
We will assume each game is independent and that the probability of a tie is fixed for every game. Then this situation follows a binomial distribution.

Let X be the number of games with a tie: then $X\,$~ $\,\text{Binomial}\,(80, 0.14)$

For a binomial distribution,

$E(X) = np = 80 \times 0.14$

and

$\sigma_X = \sqrt{np(1-p)} = \sqrt{80 \times 0.14 \times 0.86}$
• Apr 14th 2009, 10:10 PM
Allenge
Thanks for your reply, It helped me alot....I'm kinda started to get some concept.....