SOLUTION: If a student is guessing randomly on a multiple choice test with 4 possible responses per question, and 16 questions: What is the probability of getting 4 correct?

Question 1199508: If a student is guessing randomly on a multiple choice test with 4 possible responses per question, and 16 questions:
What is the probability of getting 4 correct?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

n = 16 = number of questions
p = 1/4 = 0.25 = probability of success on any question
x = 4 = number of desired successes

Use the binomial probability formula
B(x) = (n C x)*p^x*(1-p)^(n-x)
B(4) = (16 C 4)*0.25^4*(1-0.25)^(16-4)
B(4) = (1820)*0.25^4*(1-0.25)^(16-4)
B(4) = 0.22519906517119
B(4) = 0.225199

There's about a 22.5199% chance of getting exactly four correct answers.

The nCx notation refers to the nCr combination formula.

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