Question

A five question multiple choice test has 4 choices for each question and only 1 correct answer each. What is the probability of guessing at least 3 out of the 5 questions correctly?

Answer 1

Prob = 13/1024 = 0.0127

Explanation:

Prob {A correct answer} = Correct option / Total options = 1/4

Prob {A wrong answer} = Wrong options / Total options = 3/4

Prob [3 answers correct] = P (3 correct ,& 2 wrong) or P (4 correct ,& 1 wrong) or P (5 correct, & no wrong)

= [ (1/4) x (1/4) x (1/4) x (3/4) x (3/4) ] + [ (1/4) x (1/4) x (1/4) x (1/4) x (3/4) ] + [ (1/4) x (1/4) x (1/4) x (1/4) x (1/4) ]

( 9/1024 ) + ( 3/1024 ) + ( 1/1024 )

13/1024 = 0.0127