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 
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.
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