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:

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

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) = [tex]\dbinom{n}{k}\times p^{k}\times \left (1 – p \right )^{n – k}[/tex]

P(X = 2) = [tex]\dbinom{6}{2}\times \left (\dfrac{1}{5} \right )^{2}\times \left (1 – \dfrac{1}{5} \right )^{6 – 2}[/tex]

= 15×256/15625 = 768/3125 = 0.246

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