Question

An SAT test has 8 questions, each question having 5 multiple choice answers. If a student make random guesses for each answer, find the probability that: a)the number of correct answers is 7. b)the number of correct answers is at least 4. c)the number of correct answers is fewer than 3.

Answer 1

Let X be the random variable denoting the number of correct answers.

Each question have 5 multiple answer, out of which only one is correct. So probability of choosing correct answer in a single question is 1/5.

The total number of question are 8.

X will be the binomial variate with parameters n=8 and p=1/5=0.2 i.e.

X ~ Bin(8, 0.2)

The probability mass function of binomial distribution is given by

Now,

a) The probability that the number of correct answers is 7, P(X=7)

                    

                     

b) The probability that the number of correct answers is at least 4 , P(X4)

                    

                       

              

c)The probability that the number of correct answers is fewer than 3, P(X<3)