A quiz in statistics course has four multiple-choice questions, each with five possible answers. A passing grade is three or more correct answers to the four questions. Allison has not studied for the quiz. She has no idea of the correct answer to any of the questions and decides to guess at random for each.

a. Find the probability she lucks out and answers all four questions correctly.

b. Find the probability that she passes the quiz.

a) 0.0016

b) 0.0224

Step-by-step explanation:

If every question has 5 possible answers, the probability of getting the correct answer by guessing would be 0.20. The probability of getting an incorrect answer would be 0.80.

a) Find the probability she lucks out and answers all four questions correctly.

To do this, Allison would have to guess right the first, second, third AND fourth answers. Therefore, we have to multiply the probabilities:

0.20 x 0.20 x 0.20 x 0.20 = 0.0016

The probability that she answers all 4 questions correctly is 0.0016.

b) Find the probability that she passes the quiz.

To pass the quiz, she has to have three OR 4 correct answers:

The probability that she has 3 correct answers is: 0.20 x 0.20 x 0.20 x 0.80 (since she has to have 1 correct answer and 1 incorrect one) =.0064. We already calculated the probability that she guesses 4 answers correctly: 0.0016.

Now, we have to sum up these two scenarios:

0.0064 + 0.016 = 0.0224.

Thus, the probability that she passes the quiz is 0.0224