Question

A Math teacher gives a test with 5 multiple choice questions. Each question has 4 possible answers. You randomly guess the answers. Let X be the random variable defined to be the number of correct answers out of 5 test questions.

a)What probability distribution should you use to model the probabilities of this random variable. Explain and state the formula in terms of x only.

b)Create a probability distribution table for random variable X

c) Determine the probability you will pass the test.

d) If the test was 100 questions instead of 5, what would be the expected number of correct answers for this new test?

Answer 1

a)

here as number of questions are fixed, probabilty of getting a question correct is =1/4 , which is fixed and independent from question to question, this follows binomial distribution,

P(X=x)=(₅C_x)*(1/4)^x(3/4)^5-x

b)

x	P(x)
0	0.2373
1	0.3955
2	0.2637
3	0.0879
4	0.0146
5	0.0010

c)(here condition of passing is not given, if it is getting 3 or more correct)

P(passing the test) = P(X>=3)= 0.0879+0.0146+0.0010 =0.1035

d)

expected number of correct answer =np=100*1/4 =25