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

Addition Rule

Statistics

4. Probability

Addition Rule

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1:58 minutes

Problem 3.RE.39

Textbook Question

39. You are given that P(A) = 0.15 and P(B) = 0.40. Do you have enough information to find P(A or B)? Explain.

Verified step by step guidance

Step 1: Recall the formula for the probability of the union of two events, P(A or B), which is given by P(A ∪ B) = P(A) + P(B) - P(A ∩ B). This formula accounts for the overlap between events A and B to avoid double-counting.

Step 2: Substitute the given values into the formula. You are provided P(A) = 0.15 and P(B) = 0.40. However, the formula also requires the value of P(A ∩ B), the probability that both events A and B occur simultaneously.

Step 3: Assess whether P(A ∩ B) is provided or can be inferred. In this problem, P(A ∩ B) is not given, and there is no information about whether events A and B are independent or dependent. Without P(A ∩ B), you cannot calculate P(A or B) precisely.

Step 4: If events A and B were independent, you could calculate P(A ∩ B) using the formula P(A ∩ B) = P(A) × P(B). However, independence is not stated in the problem, so you cannot assume it.

Step 5: Conclude that you do not have enough information to find P(A or B) because the value of P(A ∩ B) is missing, and the relationship between events A and B (independent or dependent) is not specified.

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Key Concepts

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

Probability of Events

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1. In this context, P(A) and P(B) represent the probabilities of events A and B occurring, respectively. Understanding how to interpret these probabilities is essential for analyzing the relationship between the events.

Union of Events

The union of two events, denoted as P(A or B), represents the probability that at least one of the events occurs. To calculate this, we typically use the formula P(A or B) = P(A) + P(B) - P(A and B). However, without knowing P(A and B), we cannot determine P(A or B) accurately.

Independence of Events

Events A and B are independent if the occurrence of one does not affect the probability of the other. If A and B are independent, we can calculate P(A and B) as P(A) * P(B). However, the question does not provide information about their independence, which is crucial for determining P(A or B) without additional data.

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Textbook Question

In Exercises 25 and 26, determine whether the events are mutually exclusive. Explain your reasoning.

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Event B: Randomly select a yellow jelly bean from the jar.

Textbook Question

28. A sample of 6500 automobiles found that 1560 of the automobiles were black, 3120 of the automobiles were sedans, and 1170 of the automobiles were black sedans. Find the probability that a randomly chosen automobile from this sample is black or a sedan.

Textbook Question

In Exercises 29-32, find the probability.

31. A 12-sided die, numbered 1 to 12, is rolled. Find the probability that the roll results in an odd number or a number less than 4.

Textbook Question

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34. Find the probability of randomly selecting a school with 300 or more students.

Textbook Question

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Textbook Question

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b. Randomly selecting a person from the sample who is conservative or very conservative

Textbook Question

Politics The responses of 1500 U.S. adults to a survey that asked them to state their own political viewpoints are shown in the Pareto chart. Find the probability of each event.(Adapted from YouGov)

d. Randomly selecting a person from the sample who is either unsure or moderate

Textbook Question

22. Brexit A survey asked 1115 British adults how Britain's decision to leave the European Union has impacted the country. The results are shown in the Pareto chart. Find the

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b. Randomly selecting a British adult who feels that the move has had a very negative impact on Great Britain

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