Question

If you make random guesses for 10 multiple choice test questions each with 5

possible answers), what is the probability of getting all answers correct?

Answer 1

Solution :

Let X represents the number of correct answers in 10 multiple choice test questions.

There are 10 questions, each with 5 possible answers. For multiple choice questions, only one option is correct.

Hence, probability of guessing correct answer for a question will be 1/5 = 0.2.

Let use consider "guessing correct answer for the question" as success. So, now we have only two mutually exclusive outcomes (success and failure).

Probability of success (p) = 0.2

Number of trials (n) = 10

Since, probability of success remains constant for each of the trials, number of trials are finite, we have only two mutually exclusive outcomes for each of the trials and outcomes are independent, therefore we can consider that X follows binomial distribution.

According to binomial probability law, probability of occurrence of exactly x success in n trials is given by,

Where, p is probability of success.

We have to find P(X =10).

We have, n = 10 and p = 0.2

Using binomial probability law we get,

Hence, the probability of getting all answers correct is 0.0000001024.

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