Question

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 1

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

`P(X=3)=(14!)/(3!(14-3)!)*0.25^3*0.75^(11)`

P(X=3)=0.24