Question

MC1701: A test consists of 10 multiple choice questions, each with five possible answers, one of which is correct. To pass, a student must get at least 6 correct on the test. If a student randomly guesses at every question, what is the probability that the student fails the test?

	a.	2.6%
	b.	20%
	c.	80%
	d.	97.4%
	e.	99.4%
	f.	None of these

Answer 1

A test consists of 10 multiple choice questions, each with five possible answers,one of which is correct.

Let , x be the number of question correct.

Probability that randomly guesses question is correct = P = 1/5

n = 10

So, x follows Binomial distribution with parameter n =10 and P = 1/5.

We have to find P( x < 6 )

P( x < 6 ) = P( x <= 5 )

Using Excel,   =BINOMDIST( x, n, p, 1 )

P( x <= 5 ) = BINOMDIST( 5, 10, 1/5,1) =0.993631 99.4%

Option e is correct.