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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.
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Let X ~ Binomial(n=10, p=0.5). Then
P(X = 7) = C(10,7) (0.5)^7 (0.5)^3 = C(10,7) (0.5)^10 = 120/1024 = 15/128 ≈ 0.1171875.
P(X = 7) = C(10,7) (0.5)^7 (0.5)^3 = C(10,7) (0.5)^10 = 120/1024 = 15/128 ≈ 0.1171875.
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