Question

The probability that a tennis set will go to a tie-breaker is 19%. what is the probability that two of three sets will go to tie-breakers?

Answer 1

Answer:

The probability is:

0.087723

Step-by-step explanation:

We need to use the binomial distribution to calculate the probability.

We are given that:

The probability that a tennis set will go to a tie-breaker is 19%.

i.e. the probability is: 0.19

Also, we are asked to find  the probability that two of three sets will go to tie-breakers.

We know that the probability of binomial distribution is given as:

$P(X=k\ successes)=n_C_k\cdot p^k\cdot (1-p)^{n-k}$

where n are the total outcomes.

p is the probability of success.

and P denotes the probability.

Here we have:

p=0.19

k=2

and n=3

Hence,

$P(X=2)=3_C_2\cdot (0.19)^2\cdot (1-0.19)^{3-2}\\\\P(X=2)=\dfrac{3!}{2!\times (3-2)!}\cdot (0.19)^2\cdot (0.81)^1\\\\P(X=2)=3\cdot 0.0361\cdot 0.81\\\\P(X=2)=0.087723$

Hence, the probability that two of three sets will go a tie breaker is:

0.087723

Answer 2

Probability of  2 sets going to tie-breaker = 0.19*0.19 =  0.0361

there are 3 ways that 2 out of 3 sets are tiebreakers 
so required probability =  3 * 0.0361 = 0.1083

=   10.83%