Ch. 3 - Probability

Larson - Elementary Statistics: Picturing the World 8th Edition

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Larson 8th Edition

Ch. 3 - Probability

Problem 3.1.2c

Chapter 3, Problem 3.1.2c

2. Determine whether each number could represent the probability of an event. Explain your reasoning. c. 2.3

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Step 1: Recall the definition of probability. Probability is a measure of the likelihood of an event occurring, and it is always expressed as a number between 0 and 1, inclusive. This means 0 ≤ P(E) ≤ 1, where P(E) is the probability of an event E.

Step 2: Examine the given number, 2.3. Compare it to the range of valid probabilities (0 to 1).

Step 3: Determine whether 2.3 falls within the valid range for probabilities. Since 2.3 is greater than 1, it does not satisfy the condition 0 ≤ P(E) ≤ 1.

Step 4: Conclude that 2.3 cannot represent the probability of an event because probabilities cannot exceed 1.

Step 5: Provide reasoning: Probabilities are bounded by 0 and 1 because they represent proportions or likelihoods, and it is not possible for an event to have a likelihood greater than 100%.

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Key Concepts

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

Probability Range

Probability is a measure of the likelihood of an event occurring, and it is always expressed as a number between 0 and 1. A probability of 0 indicates that an event will not occur, while a probability of 1 indicates certainty that the event will occur. Any number outside this range, such as 2.3, cannot represent a valid probability.

Interpretation of Probability

The interpretation of probability involves understanding it as a ratio of favorable outcomes to the total number of possible outcomes. For example, if an event has a probability of 0.5, it means there is an equal chance of the event occurring or not occurring. This interpretation helps clarify why values greater than 1 are not feasible.

Types of Events

Events in probability can be classified as certain, impossible, or random. A certain event has a probability of 1, while an impossible event has a probability of 0. Understanding these classifications helps in determining whether a given number can represent a probability, as only numbers within the 0 to 1 range can correspond to valid events.

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