/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 6 A bag of candy contains 3 red ca... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 6

A bag of candy contains 3 red candies and 7 brown candies. A friend says the probability of reaching the bag without looking and pulling out a red candy is \(30 \%\) because 3 out of 10 candies are red. Is this an example of an empirical probability or a theoretical probability?

Short Answer

Expert verified
The probability described in this scenario is an example of theoretical probability.

Step by step solution

01

Understanding empirical and theoretical probabilities

Empirical probability is calculated through experiments or by collecting data, while theoretical probability is calculated by understanding the situation and mathematics. In this case, the friend didn't actually pick the candies one-by-one to gather data. Instead, a direct calculation was made knowing the total and constituent parts, which is a sign of theoretical probability calculation.
02

Analyzing the given situation

As given, there are 3 red candies and 7 brown candies in the bag. And the friend says the probability of picking a red candy is \(30\%\) because there are 3 out of a total of 10 candies that are red. Hence, the probability calculation was made theoretically - by understanding the situation and using straightforward calculation.
03

Conclusion

The friend's statement of having a \(30\%\) chance of drawing a red candy, drawn from the knowledge that 3 out of 10 candies are red, is an example of Theoretical Probability since no actual experiment or data collection was done.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

a. Explain how you could use a random number table (or the random numbers generated by software or a calculator) to simulate rolling a fair four-sided die 20 times. Assume you are interested in the probability of rolling a 1 . Then report a line or two of the random number table (or numbers generated by a computer or calculator) and the values that were obtained from it. b. Report the empirical probability of rolling a 1 on the four-sided die from part (a), and compare it with the theoretical probability of rolling a 1 .

A recent study found that highly experienced teachers may be associated with higher student achievement. Suppose fourth-grade students at an elementary school are randomly assigned to one of eight teachers. Teachers Nagle, Crouse, Warren, Tejada, and Tran are considered highly experienced. Teachers Cochran, Perry, and Rivas are considered less experienced. (Source: Papay and Kraft, "Productivity returns to experience in the teacher labor market," Journal of Public Economics, vol. \(130[2015]:\) \(105-119\) a. List the equally likely outcomes that could occur when a student is assigned to a teacher. b. What is the probability that a fourth-grade student at this school is assigned to a highly experienced teacher? c. What event is the complement of the event described in part (b)? What it the probability of this event?

The table shows the results of rolling a fair six-sided die. $$ \begin{array}{|c|c|c|c|} \hline \begin{array}{c} \text { Outcome } \\ \text { on Die } \end{array} & \mathbf{2 0} \text { Trials } & \mathbf{1 0 0} \text { Trials } & \mathbf{1 0 0 0} \text { Trials } \\ \hline 1 & 8 & 20 & 167 \\ \hline 2 & 4 & 23 & 167 \\ \hline 3 & 5 & 13 & 161 \\ \hline 4 & 1 & 13 & 166 \\ \hline 5 & 2 & 16 & 172 \\ \hline 6 & 0 & 15 & 167 \\ \hline \end{array} $$ Using the table, find the empirical probability of rolling a 1 for 20,100 , and 1000 trials. Report the theoretical probability of rolling a 1 with a fair six-sided die. Compare the empirical probabilities to the theoretical probability, and explain what they show.

Roll a fair six-sided die. a. What is the probability that the die shows an even number or a number greater than 4 on top? b. What is the probability the die shows an odd number or a number less than 3 on top?

A college conducted a student survey to learn about commute patterns. Students were given a choice of three options: car, bus, or other. When looking at the survey results, \(42 \%\) of students responded "car," and \(23 \%\) responded "bus." Assuming all students answered this survey questions, what percentage of the students responded "other"?
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.