Question

A student answers eight MCQ type of questions. Each question has five answers with only one correct answer. Compute the probability of the student answering four questions correctly.

Answer 1

Answer on Question #83341 – Math – Statistics and Probability

Question

A student answers eight MCQ type of questions. Each question has five answers with only one correct answer. Compute the probability of the student answering four questions correctly.

Solution

The probability of a student to ask each question correctly is

$$\frac {1}{5} = 0.2.$$

The number of correct answers $X$ is a binomial random variable with $n = 8$ (the total number of questions) and $p = 0.2$ (the probability of a correct answer).

Hence

$$P (X = 4) = \binom {8} {4} \cdot 0.2^{4} \cdot (1 - 0.2)^{8 - 4} = 70 \cdot 0.0016 \cdot 0.4096 = 0.0459.$$

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