Question

A student takes an 8-question, true-false exam and guesses on each question. Find the probability of passing if the lowest passing grade is 6 correct out of 8.

	a.	0.109
	b.	0.227
	c.	0.144
	d.	0.164

Answer 1

Here' the answer to the question. Please comment back in case you've doubts! Cheers! Have a good day!

A true-false exam means that for each question there are 2 options - true, and false. Each with a probability of 1/2

So, this is event follows binomial distribution.

Hence, P(the student will pass when he randomly guesses answers)
= P(scores at least 6 correctly)
= P(X=6)+P(X=7)+P(X=8)
We will use the binomial pdf function to get this.

For example:
P(X,n,p) = nCr*(p^r)*(1-p)^(n-r)
P(6,8,.5) = 8C6*(.5^6)*(.5^2)

So,
P(X=6)+P(X=7)+P(X=8)
= 8C6*(.5^6)*(.5^2) + 8C7*(.5^7)*(.5^1) + 8C8*(.5^8)*(.5^0)
= 0.144

Hence, option C. is correct