Question

Questions 5-6. Three randomly chosen fourteen-year-old junior high students who had not yet taken driver's education classes were given the written part of the Michigan Driver's Exam. Each student was graded as passing or failing the written exam. Assume each student has the same chance to pass and to fail the exam. 5. The probability no student fails equals: A. 3/8 B. 1/2 C. 1/4 D. 1/8 6. The probability at most one student passes the written test equals: A. 3/8 B. 1/2 C. 7/8 D. 3/4

          Questions 5-6. Three randomly chosen fourteen-year-old junior high students who had not yet taken driver's education classes were given the written part of the Michigan Driver's Exam. Each student was graded as passing or failing the written exam. Assume each student has the same chance to pass and to fail the exam.
5. The probability no student fails equals:
A. 3/8 B. 1/2 C. 1/4 D. 1/8
6. The probability at most one student passes the written test equals:
A. 3/8 B. 1/2 C. 7/8 D. 3/4

Show more…

Questions 5-6. Three randomly chosen fourteen-year-old junior high students who had not yet taken driver's education classes were given the written part of the Michigan Driver's Exam. Each student was graded as passing or failing the written exam. Assume each student has the same chance to pass and to fail the exam.
5. The probability no student fails equals:
A. 3/8 B. 1/2 C. 1/4 D. 1/8
6. The probability at most one student passes the written test equals:
A. 3/8 B. 1/2 C. 7/8 D. 3/4

Added by David R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Joanna Quigley

01/06/2023

Step 1

3/8 = 33% Show more…

Show all steps

lock

Thanks for your feedback!

Questions 5-6. Three randomly chosen fourteen-year-old junior high students who had not yet taken driver's education classes were given the written part of the Michigan Driver's Exam. Each student was graded as passing or failing the written exam. Assume each student has the same chance to pass and to fail the exam. 5. The probability no student fails equals: A. 3/8 B. 1/2 C. 1/4 D. 1/8 6. The probability at most one student passes the written test equals: A. 3/8 B. 1/2 C. 7/8 D. 3/4

Play audio

Feedback

Powered by NumerAI

Joanna Quigley and 87 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 We are looking at three randomly chosen students who are taking a driver's exam.

00:06 They have an equal chance of passing and of failing.

00:10 So we have three people and equals three.

00:13 And the probability of passing the exam is 0 .5, 50%.

00:18 And of failing, 50%.

00:20 For question five, we want the probability they all pass.

00:27 So the key to this question is that these are independent trials.

00:34 Each one's probability of passing does not influence the others.

00:38 So if you want to combine trials, you just need to multiply.

00:50 So for part 5, we have the probability of the first one passing, 0 .5, multiplied by the second, 0 .5, multiplied by the third, 0 .5.

01:01 0 .5 to the power of 3, which is an 8th.

01:06 So the answer is d.

01:07 1 over 2 becomes 1 over 4, becomes 1 over 8.

01:13 Part 6, we want the probability, at most, one of them passes.

01:20 So x, the number who passes, who pass is at most 1.

01:24 It could be 1, it could be 0.

01:27 So how do we find it? i'm going to make this a little bit more complicated by providing the binomial formula.

01:37 Because this is a binomial distribution.

01:40 Three independent trials, two outcomes, same probability for each.

01:45 The probability of x of them passers.

01:47 Is n choose x, p to the x, 1 minus p to the n minus x...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later