Suppose that you are taking a multiple-choice exam with five questions, each have five choices, and one of them is correct. Because you have no more time left, you cannot read the question and you decide to select your choices at random for each question. Assuming this is a binomial experiment, calculate the binomial probability of obtaining exactly three correct answers.

0.051

Step-by-step explanation:

Each question has five choices.

So , probability of correct answer is 1/5 i.e.0.2

p = 5  

Total number of questions = 5

n = 5

Let X be the number of questions that are correctly answered.  

X follows Binomial(5 , 0.2)

Using binomial probability formula ,

P(X = x) = (ₙ C ₓ) * pˣ * (1 - p)ⁿ₋ˣ ; x = 0 ,1 , 2 , , n

Find P (Exactly 3)

= P(X = 3)  

=  (₅C ₃) * 0.2³ * (1 - 0.2)⁵ ⁻ ³

= (₅ C ₃) * 0.2³ * (1 - 0.2)²

= 0.051