Question

A student is taking a mutiple choice exam in which each question has four question has four questions. Assuming that she has no knowledge of the correct answers to any of the questions, she has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box. She randomly selects one ball of each question and replaces the ball in the box. The marking on the ball will determine her anwser to the question. There are five mutiple choice questions on the exam. Complete parts (a) through (d) below.

a. what is the probability that she will get five questions correct

b. what is the probability that she will get atleast four questions correct

c. what is the probability that she will get no questions correct

d. what is the probability that she will get no more than two questions correct

Answer 1

here this is binomial with parameter n=5 and p=0.25

a)

probability that she will get five questions correct=0.25^5 =0.0010

b)

probability that she will get atleast four questions correct =P(X=4)+P(X=5)=(5C4)*(0.25)^4*0.75+0.25^5

=0.0156

c)

probability that she will get no questions correct =0.75^5 =0.2373

d)

probability that she will get no more than two questions correct =P(X<=2)

=P(X=0)+P(X=1)+P(X=2)

=0.75^5+(5C1)*0.25^1*0.75^4+(5C2)*0.25^2*0.75^3 =0.8965