Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

4. Probability

Basic Concepts of Probability

Statistics

4. Probability

Basic Concepts of Probability

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1:01 minutes

Problem 3.1.14

Textbook Question

Matching Probabilities In Exercises 11-16, match the event with its probability.
a. 0.95
b. 0.005
c. 0.25
d. 0
e. 0.375
f. 0.5
14. A game show contestant must randomly select a door. One door doubles her money while the other three doors leave her with no winnings. What is the probability she selects the
door that doubles her money?

Verified step by step guidance

Step 1: Understand the problem. The contestant is choosing randomly among four doors, where only one door doubles her money, and the other three result in no winnings. This is a classic probability problem involving equally likely outcomes.

Step 2: Recall the formula for probability of an event. The probability of an event occurring is given by the formula: P(Event) = (Number of favorable outcomes) / (Total number of possible outcomes).

Step 3: Identify the favorable outcomes. In this case, the favorable outcome is selecting the one door that doubles her money. So, the number of favorable outcomes is 1.

Step 4: Identify the total number of possible outcomes. Since there are four doors in total, the total number of possible outcomes is 4.

Step 5: Substitute the values into the probability formula. Using the formula P(Event) = (Number of favorable outcomes) / (Total number of possible outcomes), substitute 1 for the number of favorable outcomes and 4 for the total number of possible outcomes. This gives P(Event) = 1/4.

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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 an event will occur, expressed as a number between 0 and 1. A probability of 0 indicates an impossible event, while a probability of 1 indicates a certain event. In this context, the probability of selecting the winning door can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Random Selection

Random selection refers to the process of choosing an item or outcome from a set in such a way that each item has an equal chance of being selected. In the game show scenario, the contestant randomly selects one of four doors, meaning each door has an equal probability of being chosen, which is crucial for determining the probability of winning.

Favorable Outcomes

Favorable outcomes are the specific results in a probability scenario that lead to a successful event. In the case of the game show, there is one favorable outcome (selecting the door that doubles the money) out of four possible outcomes (the four doors). Understanding favorable outcomes is essential for calculating the overall probability of an event.

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Related Practice

Textbook Question

2. Determine whether each number could represent the probability of an event. Explain your reasoning. d. -0.0004

Textbook Question

3. Explain why the statement is incorrect: The probability of rain is 150%.

Textbook Question

True or False? In Exercises 7-10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

9. A probability of 1/10 indicates an unusual event.

Textbook Question

Matching Probabilities In Exercises 11-16, match the event with its probability.

a. 0.95

b. 0.005

c. 0.25

d. 0

e. 0.375

f. 0.5

11. A random number generator is used to select a number from 1 to 100. What is the probability of selecting the number 153?

Textbook Question

Identifying the Sample Space of a Probability Experiment In Exercises 25-32, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate.

25. Guessing the initial of a student's middle name

Textbook Question

28. Identifying a person's eye color (brown, blue, green, hazel, gray, other) and hair color (black, brown, blonde, red, other).

Textbook Question

Identifying Simple Events In Exercises 33-36, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning.

34. A spreadsheet is used to randomly generate a number from 1 to 4000. Event B is generating a number less than 500.

Textbook Question

Finding Classical Probabilities In Exercises 41-46, a probability experiment consists of rolling a 12-sided die numbered 1 to 12. Find the probability of the event.

43. Event C: rolling a number greater than 4

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