Question

A multiple choice test consists of 10 questions each with four choices (a,b,c,d) for each question. If a student must get at least 7 correct to pass the test, what is the probability that a student could pass the exam simply by guessing? Find your answer to 4 decimal places.

Answer 1

Solution:- Given that n = 10, p = 1/4 = 0.25

P(X >= 7) = 0.0035

Explanation :-

Therefore, we get that Pr[X27) = $P¢¢X = i) = $ (3) (1 –pjai This implies that Pr(X > 7) = Pr( X = 7) + Pr( X = 8) + Pr( X = 9) + Pr( X = 10) = (19) 0.25" x 0.7510-7 + (19) 0.259 x 0.7510-8 + (*) 0.25" x 0.7510-9 + (10) 0.250 x 0.7510-10 = 0.0031 +0.0004 +0+0 = 0.0035 which means that the probability we are looking for is Pr(X > 7) = 0.0035.