Suppose that you are taking a multiple-choice exam with five questions, each hav

Step 1
Obtain the binomial probability of obtaining exactly one correct answer.
The binomial probability of obtaining exactly one correct answer is obtained below as follows:
Let X denotes the number of correct answers which follows binomial distribution with the probability of success 1/5 with the number of questions randomly selected is 5.
That is, \(\displaystyle{n}={5},{p}={\frac{{{1}}}{{{5}}}},{q}={\frac{{{4}}}{{{5}}}}\)
The probibility distribution is given by,
\(P(X=x)=\left(\begin{array}{c}n\\ x\end{array}\right) p^{x}(1-p)^{n-x}; here\ x=0,1,2, \cdots, n\ for\ 0 \leq p \leq 1\)
Where n is the number of trials and p is the probability of success for each trial.
Step 2
The required probability is,
Use Excel to obtain the probability value for x equals 1.
Follow the instruction to obtain the P-value:
1. Open EXCEL
2. Go to Formula bar.
3. In formula bar enter the function as“=BINOMDIST”
4. Enter the number of success as 1
5. Enter the Trails as 5
6. Enter the probability as 0.20
7. Enter the cumulative as False
8. Click enter.
EXCEL output:
From the Excel output, the P-value is 0.4096.
The binomial probability of obtaining exactly one correct answer is 0.4096.