Question

Clovis will take a 12- question multiple-choice test in psychology. Regrettably he is totally unprepared and will randomly guess the answers. Each problem has 4 answer choices (A, B, C, and D). Let X be the number of correct guesses on the test. a. What is the probability distribution of X? X~ b. What is ?, the expected number of correct answers Clovis will get? c. What is the probability that Clovis will get exactly six correct answers? d. Clovis must get at least nine correct answers to pass the test. What is the probability that he will pass the test?

Answer 1

Number of question: n = 12

Total number of options= 4

Prbability of correct guess: p = 1/4 = 0.25

Let X be the number of correct guesses.

a. The probability distribution of X

P.m.f of x is

b. Expected number of correct answers

c.

Probability that Clovis will get excatly six correct answers = 0.04

d. Clovis must get at least nine correct answers to pass the test.

  

= 0.00035 + 0.000035+0.0000021+0.00000006 = 0.00039

Probability that he will pass the test = 0.00039