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,
[tex]P(Hit)=1-P(NoHit)[/tex]Therefore, we need to calculate the probability of not hitting the ball within the first 5 at-bats.
The binomial distribution states that
[tex]\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}[/tex]Thus, in our case,
[tex]P(k=0)=(5Binomial0)(0.341)^0(0.659)^5=1*1*0.124287...[/tex]Then,
[tex]P(Hit)=1-0.124287...\approx0.876[/tex]