Question

Beth is taking a 7​-question ​multiple-choice test for which each question has three answer​ choices, only one of which is correct. Beth decides on answers by rolling a fair die and marking the first answer choice if the die shows 1 or​ 2, the second if it shows 3 or​ 4, and the third if it shows 5 or 6. Find the probability that she gets exactly 5 correct answers.

Answer 1

Given:- n=7 ,where n is multiple choice questions

Beth roll dice and answer the MCQ,.

if beth roll (1 or 2 ) :- mark 1st answer choice

If beth roll (3 or 4) :- mark 2nd answer choice

If beth roll (5 or 6) :- mark 3rd answer choice

Solution:-

x = number of correct answer

n =7

Probability of choosing correct answer (p)=2/6 =1/3

Here trials are independent from each other and probability of choosing correct answer is constant for each trials. That's why we use binomial distribution.

therefore, q=1-p =2/3

Probability that she get exactly 5 correct answer:-

P(x=5) =  

=0.0369

Hence, the probability that she get exactly 5 correct answer is 0.0369