A quiz consists of 10 multiple-choice questions with 5 choices for each question. Suppose a student is sure of the first 5 answers and has each of the last 5 questions narrowed to 3 of the possible 5 choices. If the student guesses among the narrowed choices on the last 5 questions, find the probability of getting at least a C (at least 70%). Round your answer to four decimal places.
A)Pr(Grade ≥ C) = 0.0412
B)Pr(Grade ≥ C) = 0.4200
C)Pr(Grade ≥ C) = 0.5391
D)Pr(Grade ≥ C) = 0.4609
E)Pr(Grade ≥ C) = 0.0163

Question

A quiz consists of 10 multiple-choice questions with 5 choices for each question. Suppose a student is sure of the first 5 answers and has each of the last 5 questions narrowed to 3 of the possible 5 choices. If the student guesses among the narrowed choices on the last 5 questions, find the probability of getting at least a C (at least 70%). Round your answer to four decimal places. ​
A)Pr(Grade ≥ C) = 0.0412
B)Pr(Grade ≥ C) = 0.4200
C)Pr(Grade ≥ C) = 0.5391
D)Pr(Grade ≥ C) = 0.4609
E)Pr(Grade ≥ C) = 0.0163

Quizplus · Accepted Answer

The student is sure of the first 5 answers, so they will get those right. For the last 5 questions, they have narrowed down to 3 choices, so the probability of getting one of those choices right is 1/3. The probability of getting all 5 narrowed choices right is (1/3)^5. To find the probability of getting at least a C (70% or higher), we need to find the probability of getting 7 or more questions correct out of 10 (since 7/10 is 70%).

We can use the binomial probability formula to calculate this:

P(X ≥ 7) = 1 - P(X < 7)

where X is the number of questions the student gets right and P(X < 7) is the probability of getting less than 7 questions right.

P(X < 7) = binomcdf(5, 1/3, 6)

Using a calculator or software to compute this, we get:

P(X < 7) = 0.4609

Therefore,

P(X ≥ 7) = 1 - P(X < 7) = 0.5391

So the answer is Choice C.

A Quiz Consists of 10 Multiple-Choice Questions with 5 Choices