Question

Henry had a batting average of 0.341 last season (out of 1000 at-bats, he had 341 hits). Given that thisbatting average will stay the same this year, answer the following questions,What is the probabilitythat his first hit willoccur within his first 5at-bats? Answer choice. 0.654. 0.765. 0.821. 0.876

Answer 1

The probability of a successful batting is 0.341; we need to find the probability of at least 1 hit within the first 5 at-bats; thus,

`P(Hit)=1-P(NoHit)`

Therefore, we need to calculate the probability of not hitting the ball within the first 5 at-bats.

The binomial distribution states that

`\begin{gathered} P(X=k)=(nBinomialk)p^k(1-p)^(n-k) \\ n\rightarrow\text{ total number of trials} \\ k\rightarrow\text{ number of successful trials} \\ p\rightarrow\text{ probability of a successful trial} \end{gathered}`

Thus, in our case,

`P(k=0)=(5Binomial0)(0.341)^0(0.659)^5=1*1*0.124287...`

Then,

`P(Hit)=1-0.124287...\approx0.876`

Therefore, the answer is 0.876