Lesson 19.1 Probability Distributions

Last updated over 1 year ago

11 questions

Note from the author:

I can define and display probability distributions for discrete random variables to model real-world scenarios or probability experiments.

Instructions

I can define and display probability distributions for discrete random variables to model real-world scenarios or probability experiments.

Multiple Choice

For Problems 1–6, use the following situation. A teacher gives students a multiple-choice quiz with 6 questions. Each question has 3 choices: A, B, and C.

How can you use Pascal’s Triangle to determine how many different ways a student can get exactly 4 of the 6 questions correct?

How many different ways are possible?

Suppose a student was unprepared for the quiz and guessed an answer for each question. If the student is equally likely to choose any of the answers for all questions, what is the probability that the student answers 5 questions correctly?

If a student is equally likely to choose any of the answers for all questions, what is the probability that the student answers no more than 2 questions correctly?

Marissa has correctly answered 80% of all multiple-choice questions on quizzes in the class this year. Make a probability distribution showing how many questions you would expect Marissa to answer correctly on this quiz.

Deidre has correctly answered 90% of all multiple-choice questions on quizzes in the class this year. How would a probability distribution showing the number of questions you would expect her to answer correctly on this quiz compare to the distribution for Marissa?

Let's Go Charlie Conway

If a hockey game is tied after overtime, five rounds of alternating penalty shots decide the winner. If one team has scored more goals after each team has taken their 5 penalty shots, then that team wins, and the game is over.

Find the probability that Team A’s opponent, Team B, scores at least once in their 5 penalty shots.

Team A scored on 3 of their 5 penalty shots. What is the probability that Team B wins the game after their 5 penalty shots?

Manufacturing

A machine produces acceptable parts with 97% reliability.

Lesson 19.1 Probability Distributions

How can you use Pascal’s Triangle to determine how many different ways a student can get exactly 4 of the 6 questions correct?

How many different ways are possible?

Suppose a student was unprepared for the quiz and guessed an answer for each question. If the student is equally likely to choose any of the answers for all questions, what is the probability that the student answers 5 questions correctly?

If a student is equally likely to choose any of the answers for all questions, what is the probability that the student answers no more than 2 questions correctly?

Marissa has correctly answered 80% of all multiple-choice questions on quizzes in the class this year. Make a probability distribution showing how many questions you would expect Marissa to answer correctly on this quiz.

Deidre has correctly answered 90% of all multiple-choice questions on quizzes in the class this year. How would a probability distribution showing the number of questions you would expect her to answer correctly on this quiz compare to the distribution for Marissa?

Find the probability that Team A’s opponent, Team B, scores at least once in their 5 penalty shots.

Team A scored on 3 of their 5 penalty shots. What is the probability that Team B wins the game after their 5 penalty shots?

What is the probability that the machine makes exactly 18 acceptable parts in one minute?

What is the probability that the machine makes more than 18 acceptable parts in one minute?

What is the probability that the machine makes fewer than 18 acceptable parts in one minute?