Question

Probability of guessing correctly atleast 7 out of 10 answers in a ‘True’ or ‘False’ test is equal to ______.

Options

• `11/64`

• `11/32`

• `11/16`

• `27/32`

Answer 1

Probability of guessing correctly atleast 7 out of 10 answers in a ‘True’ or ‘False’ test is equal to `underlinebb(11/64)`.

Explanation:

In every true and false question, the probability of guessing correctly, p = `1/2` and the probability of guessing wrongly, q = `1/2`.

Here, n = 10

∴ The probability of atleast 7 correctly guessing

= P(X ≥ 7)

= P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

= `""^10C_7 (1/2)^7 (1/2)^3 + ""^10C_8 (1/2)^8 (1/2)^2 + ""^10C_9 (1/2)^9 (1/2)^1 + ""^10C_10 (1/2)^10` ...`[∵ P(x = r) = ""^nC_r p^rq^(n - r)]`

= `120(1/2)^10 + 45(1/2)^10 + 10(1/2)^10 + 1(1/2)^10`

= `(120 + 45 + 10 + 1)/2^10`

= `176/1024`

= `11/64`