Question

The probability of guessing correctly at least 8 out of 10 answers on a true-false type-examination is ______.

Options

• `7/64`

• `7/128`

• `45/1024`

• `7/41`

Answer 1

The probability of guessing correctly at least 8 out of 10 answers on a true-false type-examination is `7/128`.

Explanation:

Here, n = 10

p = `1/2` and q = `1/2`  ....(For true/false questions)

And r ≥ 8 i.e. 8, 9, 10

∴ P(X ≥ 8) = P(x = 8) + P(x = 9) + P(x = 10)

= `""^10"C"_8 (1/2)^8 (1/2)^2 + ""^10"C"_9 (1/2)^9 (1/2) + ""^10"C"_10 (1/2)^10 (1/2)^0`

= `45*(1/2)^10 + 10*(1/2)^10 + (1/2)^10 + (1/2)^10`

= `(1/2)^10`  (45 + 10 + 1)

= `56 xx 1/1024`

= `7/128`