True or False? In Exercises 7-10, determine whether the statement...

4. Probability

Basic Concepts of Probability

Statistics

4. Probability

Basic Concepts of Probability

1:21 minutes

Problem 3.1.9

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.

Verified step by step guidance

Step 1: Understand the concept of an 'unusual event' in probability. In statistics, an event is typically considered unusual if its probability is less than or equal to 0.05 (5%). This threshold is commonly used but can vary depending on context.

Step 2: Convert the given probability of 1/10 into decimal form for easier comparison. The probability 1/10 is equivalent to 0.1 (10%).

Step 3: Compare the probability of 0.1 to the threshold of 0.05. Since 0.1 is greater than 0.05, the event is not considered unusual based on the standard threshold.

Step 4: Rewrite the statement if it is false. The correct statement would be: 'A probability of 1/10 does not indicate an unusual event.'

Step 5: Conclude the reasoning by emphasizing that the classification of an event as unusual depends on the probability threshold, which is typically 0.05 in most statistical contexts.

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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. A probability of 0 indicates that an event will not happen, while a probability of 1 indicates certainty. Probabilities can also be expressed as fractions, percentages, or decimals, and they help in assessing the risk and making informed decisions.

Unusual Events

An unusual event is typically defined as one that has a low probability of occurring. In many contexts, events with probabilities less than 0.05 (or 5%) are considered unusual. However, the threshold for what constitutes 'unusual' can vary depending on the specific context and the norms of the field of study.

Interpreting Probability Values

Interpreting probability values involves understanding what different probabilities signify about the likelihood of events. A probability of 1/10 (or 0.1) suggests that the event is not very likely to occur, but it is not necessarily unusual. This interpretation is crucial for accurately assessing statements about events and their probabilities.

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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.