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?
Probability of 2 sets going to tie-breaker = 0.190.19 = 0.0361
there are 3 ways that 2 out of 3 sets are tiebreakers
so required probability = 3 0.0361 = 0.1083
= 10.83%
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