Question

In a multiple-choice question, there are three options out of which only one is correct. A person is guessing the answer at random. If there are 7 such questions, then the probability that he will get exactly 4 correct answers is ______ 

Options

• `8/3^7`

• `16/3^7`

• `280/3^7`

• `560/3^7`

Answer 1

In a multiple-choice question, there are three options out of which only one is correct. A person is guessing the answer at random. If there are 7 such questions, then the probability that he will get exactly 4 correct answers is `underline(280/3^7)`.

Explanation:

The probability of correct guess is p = `1/3`

∴ q = `1 - 1/3 = 2/3`

Also, n = 7

∴ Required probability = P (X = 4)

= `""^7"C"_4 (1/3)^4(2/3)^3`

= `280/3^7`