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If a student randomly guesses five multiple-choice questions, each with five possible choices, what is the probability of getting exactly two correct?
  1. 128/625 (20.48%)
  2. 64/625 (10.24%)
  3. 256/625 (40.96%)
  4. None of these
Explanation

n = 5 questions  

k = 2 correct  

p = 1/5 = 0.2 probability correct  

q = 4/5 = 0.8 probability wrong  

Formula: P = C(n,k) _ p^k _ q^(n-k)  

P = C(5,2) _ (0.2)^2 _ (0.8)^3  

P = 10 _ 0.04 _ 0.512  

P = 0.2048  

So probability of getting exactly 2 correct = 0.2048 = 128/625 (20.48%)


Last verified on 11-07-2026

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  1. 128/625 (20.48%)
  2. 64/625 (10.24%)
  3. 256/625 (40.96%)
  4. None of these
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