Answer:
The probability that he/she gets exactly 3 correct answers is 0.2013
Explanation:
In this question, we are tasked with calculating the probability that out of 10 questions, a student who is a random guesser, gets exactly 3 correct questions given that the test is a multiple-choice test with 5 options each.
The total number of questions n = 10
Now let the probability of answering one question correctly be p, since there is exactly one correct answer out of 5 options, this probability is equal to 1/5
Let the probability of picking an incorrect option be q, since there are 4 incorrect options, the probability of selecting an incorrect option is 4/5
Now, we compute the probability of getting exactly 3 correct options using the Bernoulli test as follows;
Probability that he/she gets exactly 3 correct answers P(X=3) =nCx × p^x × q^(n-x)
→ 10C3 × (1/5)^3 × (4/5)^7 = 0.2013