Question

You take a quiz that consists of 5 multiple-choice questions. Each question has 5 possible answers, only one of which is correct. You will randomly guess the answer to each question. The random variable represents the number of correct answers. Construct the probability distribution for this random variable.

Answer 1

Solution:
Given in the question
Number of multiple choice question = 5
Every question have 5 possible answer and only one of which is correct
P(Correct answer) = 1/5 = 0.2
Here X = Number of correct answers
All question answers are independent to each other so probability distribution can be constructed as
We will use binomial distribution as follows
P(X = n|N,p) = NCn*(p^n)*((1-p)^(N-n))
P(0 Correct answer) = 5C0*(0.2^0)*((1-0.2)^(5-0)) = 0.3277
P(1 Correct answer) = 5C1*(0.2^1)*((1-0.2)^(5-1)) = 0.4096
P(2 Correct answer) = 5C2*(0.2^2)*((1-0.2)^(5-2)) = 0.2048
P(3 Correct answer) = 5C3*(0.2^3)*((1-0.2)^(5-3)) = 0.0512
P(4 Correct answer) = 5C4*(0.2^4)*((1-0.2)^(5-4)) = 0.0064
P(5 Correct answer) = 5C5*(0.2^5)*((1-0.2)^(5-5)) = 0.0003

Probability distribution for this random variable is

No. Of correct Answer(X)	P(X)
0	0.3277
1	0.4096
2	0.2048
3	0.0512
4	0.0064
5	0.0003