Question

Find the probability of guessing correctly at least nine out of ten answers in a "true" or "false" objective test

Answer 1

Let X denote the number of correct answers.

P(answer is correct) = p = `1/2`

∴ q = 1 – p

= `1 - 1/2`

= `1/2`

Given, n = 10

∴ `"X" ∼ (10, 1/2)`

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

P(X = x) = `""^10"C"_x(1/2)^x (1/2)^(10 - x), x = 0, 1, ..., 10`

P(at least nine answers are correct)

= P(X ≥ 9)

= P(X = 9) + P(X = 10)

= `""^10"C"_9 (1/2)^9 (1/2) + ""^10"C"_10(1/2)^10`

= `10/2^10 + 1/2^10`

= `11/2^10`

= `11/1024`