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

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

Step-by-step 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}* p^(k)* \left (1 - p \right )^(n - k)`

P(X = 2) =
`\dbinom{6}{2}* \left ((1)/(5) \right )^(2)* \left (1 - (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.