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A quiz consists of 14 questions, four possible answers are provided for each question, with one of them being the correct answer. If I randomly choose an answer foreach question, what is the probability that I answer exactly 3 questions correctly? Enter answer as a decimal rounded to two digits after the decimal point. Forexample, if your calculated answer is 0.1356, enter 0.14, DO NOT enter 13.56% or 0.1356 or 13,56.

Answer :

In this problem

we have a binomial probability distribution

where

n=14

X=3

p=1/4=0.25 (probability of success)

q=0.75 (probability of fail)

substitute

[tex]P(X=3)=\frac{14!}{3!(14-3)!}*0.25^3*0.75^{11}[/tex]

P(X=3)=0.24

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