Question

A student randomly guesses on 10 true or false questions. Use the binomial model to find the probability that the student gets 7 out of the 10 questions right.
A. 11.8%
B. 20.9%
C. 32.4%
D. 50%

Answer 1

Let X ~ Binomial(n=10, p=0.5).
P(X=7) = C(10,7) (0.5)^7 (0.5)^3 = C(10,7) / 2^10 = 120 / 1024 ≈ 0.1171875 ≈ 11.8%.

Answer: A.