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

Suppose that you are taking a multiple-choice exam with five questions, each have five choices, and one of them is correct. Because you have no more time left, you cannot read the question and you decide to select your choices at random for each question. Assuming this is a binomial experiment, calculate the binomial probability of obtaining exactly one correct answer.
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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.