Question

A test consists of 18

a. True
b. False questions. to pass the test a student must answer at least 13 questions correctly. if a student guesses on each question, what is the probability that the student will pass the test?

Answer 1

Number of questions = 18

Find each of the probability :
P(13 correct) = 18C13 (0.5)¹⁸ = 8568 / 262144
P(14 correct) = 18C14 (0.5)¹⁸ = 3060 / 262144
P(15 correct) = 18C15 (0.5)¹⁸ = 816 / 262144
P(16 correct) = 18C16 (0.5)¹⁸ = 153 / 262144
P(17 correct) = 18C17 (0.5)¹⁸ = 18 / 262144
P(18 correct) = 18C18 (0.5)¹⁸ = 1 / 262144

Find sum of the above probability :
Find P( ≥ 13 correct) = ( 8568 + 3060 + 816 + 153 + 18 + 1) / 262144
Find P( ≥ 13 correct) =12616/262144
Find P( ≥ 13 correct) = 1577/32768
Find P( ≥ 13 correct) = 0.048

Answer: 0.048

Answer 2

A. True. about 10% because if you guess on every question you might not pass the test.