Question

On a five question multiple choice test there are five possible answers of which one is correct. If a student guesses randomly and independently what is the probability that she is correct only on two questions?​

Answer 1

Answer:

The probability that she is correct on only two questions is 0.246

Explanation:

The probability of getting an answer correct = 1/5

The probability of getting only two questions correctly

By binomial trials, we have;

P(X = K) = $\dbinom{n}{k}\times p^{k}\times \left (1 - p \right )^{n - k}$

P(X = 2) = $\dbinom{6}{2}\times \left (\dfrac{1}{5} \right )^{2}\times \left (1 - \dfrac{1}{5} \right )^{6 - 2}$

= 15×256/15625 = 768/3125 = 0.246

Therefore, the probability that she is correct on only two questions = 0.246.