Question

There are five multiple choice questions on an exam, each having responses a, b, c, and d. Each question is worth 5 points, and only one option per question is correct. Suppose the student guesses the answer to cach question, and these guesses, from question to question, are independent. If the student needs at least 20 points to pass the test, the probability that the student passes is closest to: O 0.0146 O 0.0156 0.001

Answer 1

The probability of one question right is 1/4 since there are 4 options and only 1 is correct, that is, 25% or 0.25

Similarly, the probability of getting an answer wrong is 75% or 0.75

To get at least 20 points to pass the test, the student has to answer 4 questions out of 5 correctly. This is since each question has 5 points and 4X5= 20 points.

The probability of getting any 4 out of 5 right is the sum of the probabilities of the 5 different orders in which one can choose 4 right and 1 wrong:

(.25)*(.25)*(.25)*(.25)*(.75) + (.25)*(.25)*(.25)*(.75)*(.25) + (.25)*(.25)*(.75)*(.25)*(.25) + (.25)*(.75)*(.25)*(.25)*(.25) + (.75)*(.25)*(.25)*(.25)*(.25)

= 5 different ways to order (.25)*(.25)*(.25)*(.25)*(.75)

= 5*0.0029296875

= 1.4648% or 0.0146

Thus option A is correct : 0.0146

Answer 2

The question asks for at least  so we need to account for the probability he gets all 5 questions right so it 0.0156