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Binomial & Poisson Distributions · Question 21 of 68

What is the probability that the guessing student gets exactly one quiz answer right?

Question 21

MediumOriginal question

A quiz has 5 questions, each with 4 options of which one is right. A student who has not studied guesses every answer at random.

What is the probability that the guessing student gets exactly one quiz answer right?

Options for question 21

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. P(X=1)=5C1(14)(34)4P(X = 1) = {}^{5}C_{1}\left(\frac{1}{4}\right)\left(\frac{3}{4}\right)^{4}.

  2. 5×14×81256=4051,0245 \times \frac{1}{4} \times \frac{81}{256} = \frac{405}{1{,}024}.

Worth noting

811,024\frac{81}{1{,}024} leaves out 5C1=5{}^{5}C_{1} = 5, the five places the right answer could be.

Concept
Exactly one success
Typical time
120 s
Your time
—
The rule this testsBinomial probabilities
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