Question

A multiple-choice test in which each question has 4 choices only one of which is correct. Assume that 9 questions are answered by guessing randomly. What is the probability of getting exactly 6 correct answers?

Answer 1

Therefore, the probability is P=0.0084.

Explanation:

We know that a multiple-choice test in which each question has 4 choices only one of which is correct. Assume that 9 questions are answered by guessing randomly.

Because we have 4 choices only one of which is correct, we get that p=0.25 and q=0.75.

We calculate the probability of getting exactly 6 correct answers.

n=9 and k=6.

`P=C_k^n\cdot p^k\cdot q^(n-k)\\\\P=C_6^9\cdot 0.25^6\cdot 0.75^3\\\\P=84\cdot 0.0001\\\\P=0.0084`

Therefore, the probability is P=0.0084.