Question

A student is taking a multiple-choice exam in which each question has four choices. Assume that the student 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 for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are five multiple-choice questions on the exam. What is the probability that she will get

A. five quesions correct?
B. At least four questions correct?
C. No questions correct?
d. No more than two questions correct?

Answer 1

Concepts and reason

A binomial distribution describes the possible number of times that a particular event will occur in a sequence of observation.

The conditions for the binomial distribution is,

A trial has only two possible outcomes namely success or failure.

There is fixed number of identical trials.

The trials of the experiment are independent of each other,

Fundamentals

The probability distribution function of Binomial distribution is,

Here,

The number of trials

The probability of success

$q=1-p= $ The probability of failure

a)

The probability of each question correct is, $p==0.25 $

The total number of questions is,

Calculate the probability that five questions correct.

(b)

Calculate the probability that at least four questions correct.

c)

Calculate the probability of no questions correct.

d)

Calculate the probability of no more than two questions correct.

Ans: Part a

The probability that five questions correct is 0.00098.

Part b

The probability that at least four questions correct is 0.0156.

Part c

The probability of no questions correct is 0.2373.

Part d

The probability of no more than two questions correct is 0.8965.