Oil a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

Explanation

The repeated guessing of correct answers from multiple-choice questions is Bernoulli trials.

Let ` X ` represent the number of correct answers by guessing in the set of `5` multiple-choice questions.

Probability of getting a correct answer is, `p=frac{1}{3}`

`therefore q=1-p=1-frac{1}{3}=frac{2}{3}`

Clearly, `X` has a binomial distribution with `n=5 and p=frac{1}{3}.`

The p.m.f. of `X` is given by

`{P}({X}={x})={ }^{n} C_{x} p^{x} q^{n-x}, {x}=0,1,2,4,5`

`i.e. {p}({x})=^{n} C_{x}(frac{1}{3})^{x}(frac{2}{3})^{5-x} {x}=0,1,2,3,4,5`

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