Answer:
The probability that he has exactly 2 hits in his next 7 at-bats is 0.3115.
Step-by-step explanation:
We are given that a baseball player has a batting average of 0.25 and we have to find the probability that he has exactly 2 hits in his next 7 at-bats.
Let X = <u><em>Number of hits made by a baseball player</em></u>
The above situation can be represented through binomial distribution;
![P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......](https://tex.z-dn.net/?f=P%28X%20%3D%20r%29%20%3D%20%5Cbinom%7Bn%7D%7Br%7D%5Ctimes%20p%5E%7Br%7D%20%5Ctimes%20%281-p%29%5E%7Bn-r%7D%3B%20x%20%3D%200%2C1%2C2%2C......)
where, n = number of trials (samples) taken = 7 at-bats
r = number of success = exactly 2 hits
p = probability of success which in our question is batting average
of a baseball player, i.e; p = 0.25
SO, X ~ Binom(n = 7, p = 0.25)
Now, the probability that he has exactly 2 hits in his next 7 at-bats is given by = P(X = 2)
P(X = 2) =
=
= <u>0.3115</u>