Table of contents

1. Intro to Stats and Collecting Data1h 14m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically2h 5m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables3h 6m
6. Normal Distribution and Continuous Random Variables2h 11m
7. Sampling Distributions & Confidence Intervals: Mean3h 23m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample3h 29m
10. Hypothesis Testing for Two Samples4h 50m
11. Correlation1h 6m
12. Regression1h 50m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 57m

4. Probability

Complements

Statistics

4. Probability

Complements

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2:18 minutes

Problem 4.2.1

Textbook Question

Notation When randomly selecting a new smartphone, D denotes the event that it has a manufacturing defect. What do P(D) and P(D) represent?

Verified step by step guidance

Step 1: Understand the notation. In probability, 'P(D)' represents the probability of event 'D' occurring. Here, 'D' is the event that a randomly selected smartphone has a manufacturing defect.

Step 2: Clarify the meaning of 'P(D)'. It quantifies the likelihood of the event 'D' happening, expressed as a value between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.

Step 3: Recognize that 'P(D)' is a mathematical representation of the probability. For example, if 5% of smartphones have defects, then P(D) = 0.05.

Step 4: If the problem also refers to 'P(D)', it is likely asking for the same probability value, as 'P(D)' is the standard notation for the probability of event 'D'.

Step 5: To calculate P(D) in practice, you would divide the number of defective smartphones by the total number of smartphones in the sample or population, using the formula:

P (D) = \frac{Number of defective smartphones}{Total number of smartphones}

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, P(D) represents the probability that a randomly selected smartphone has a manufacturing defect. Understanding probability is essential for interpreting the likelihood of events in statistics.

Event

An event in probability is a specific outcome or a set of outcomes from a random experiment. In this case, D is the event that a smartphone has a manufacturing defect. Recognizing events helps in calculating probabilities and understanding the context of statistical analysis.

Notation in Probability

Notation in probability provides a standardized way to represent events and their probabilities. P(D) specifically denotes the probability of event D occurring. Familiarity with this notation is crucial for effectively communicating and solving problems in statistics.

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Related Practice

Multiple Choice

When drawing a marble out of a bag of red, green, and yellow marbles 8 times, a red or yellow marble is drawn 6 times. What is the probability of drawing a green marble?

Multiple Choice

A weatherman states that the probability that it will rain tomorrow is 10%, or 0.1, & the probability that it will snow is 25%, or 0.25. What is the probability that it will not rain or snow?

Textbook Question

California Lottery Let A denote the event of placing a $1 straight bet on the California Daily 4 lottery and winning. There are 10,000 different ways that you can select the four digits (with repetition allowed) in this lottery, and only one of those four-digit numbers will be the winner. What is the value of P(A)? What is the value of P(Abar)?

Textbook Question

Laundry Symbols Based on a New Generation of Stains survey, 13% of U.S. adults know that the care-instruction symbol on clothing means that any bleach can be used. Find the probability of randomly selecting an adult in the U.S. who does not know that.

Textbook Question

Women in Movies In a recent year, speaking characters in movies were 68.2% male. What is the probability of randomly selecting a character with a speaking part and getting a female? What should be the value of that probability?

Textbook Question

Births in Vietnam In Vietnam, the probability of a baby being a boy is 0.526 (based on the data available at this writing). For a family having four children, find the following.

b. The probability that all four children are girls.

Textbook Question

Denomination Effect

In Exercises 13–16, use the data in the following table. In an experiment to study the effects of using four quarters versus a $1 bill, some college students were given four quarters and others were given a $1 bill, and they could either keep the money or spend it on gum. The results are summarized in the table (based on data from “The Denomination Effect,” by Priya Raghubir and Joydeep Srivastava, Journal of Consumer Research, Vol. 36).

Denomination Effect

b. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters.

Textbook Question

Denomination Effect

a. Find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill.

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