Question

A student takes an exam containing 13 true or false questions. If the student guesses, what is the probability that he will get exactly 2 questions right? Round your answer to four decimal places.

Answer 1

Solution:

There are two options for each question. TRUE and FALSE

So

P(Getting question RIGHT ) = 1/2 = 0.5

p = 0.5

Now , there are 13 questions in the exam.

n = 13

Let X be the number of the right questions .

X follows Binomial(13 , 0.5)

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x} ; x = 0 ,1 , 2 , ....., n

P(get exactly 2 questions right)

= P(X = 2)

= (₁₃ C ₂) * 0.5² * (1 - 0.5)^{13 - 2}   

= {13!/[2!*11!] } 0.5² * (0.5)¹¹

= 0.0095