Question

An archer is able to hit the bullseye 55% of the time. If she shoots 8 arrows, what isthe probability that she gets exactly 5 bullseyes?Round your answer to 4 decimal places and include a 0 before the decimal. Forexample, 0.1534.

Answer 1

Given,

`\begin{gathered} n=8 \\ p=(55)/(100) \\ p=0.55\% \end{gathered}`

The probability mass function is calculated by the given formula,

`P(X=x)=^nC_xp^x^{}(1-p)^(n-x)^{}`

Here, x = 0, 1, 2, 3.....n.

Here, n = 8 and x = 5.

Calculate the probability that she gets exactly 5 bullseyes.

`\begin{gathered} P(X=5)=^8C_5(0.55)^5(1-0.55)^(8-5) \\ P(X=5)=^8C_5(0.55)^5(1-0.55)^3 \\ P(X=5)=(8*7*6)/(3*2*1)(0.55)^5(0.45)^3 \\ P(X=5)=0.256 \end{gathered}`

Therefore, the probability that she gets exactly 5 bullseyes is 0.256