Question

You are about to take a 16-question true-false test. Assume you answer all 16 questions by guessing.

What is the probability of getting more than 10 questions correct?

Answer 1

Here, n = 16, p = 0.5, (1 - p) = 0.5 and x = 10
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <= 10).
P(X <= 10) = (16C0 * 0.5^0 * 0.5^16) + (16C1 * 0.5^1 * 0.5^15) + (16C2 * 0.5^2 * 0.5^14) + (16C3 * 0.5^3 * 0.5^13) + (16C4 * 0.5^4 * 0.5^12) + (16C5 * 0.5^5 * 0.5^11) + (16C6 * 0.5^6 * 0.5^10) + (16C7 * 0.5^7 * 0.5^9) + (16C8 * 0.5^8 * 0.5^8) + (16C9 * 0.5^9 * 0.5^7) + (16C10 * 0.5^10 * 0.5^6)
P(X <= 10) = 0 + 0.0002 + 0.0018 + 0.0085 + 0.0278 + 0.0667 + 0.1222 + 0.1746 + 0.1964 + 0.1746 + 0.1222
P(X <= 10) = 0.895

Required probability, P(X > 10) = 1 - P(X <= 10)
= 1 - 0.895
= 0.105