Writing In Exercises 89 and 90, write a statement that represents...

4. Probability

Complements

Statistics

4. Probability

Complements

2:07 minutes

Problem 3.1.90

Textbook Question

Writing In Exercises 89 and 90, write a statement that represents the complement of the probability.
90. The probability of randomly choosing a car with more than one cause for showing its "CHECK ENGINE" light from the population of vehicles showing "CHECK ENGINE" lights.

Verified step by step guidance

Understand the concept of complement probability: The complement of a probability is the likelihood of the opposite event occurring. If the probability of an event is P(A), the complement is calculated as 1 - P(A).

Identify the event in the problem: The event described is 'randomly choosing a car with more than one cause for showing its "CHECK ENGINE" light.'

Define the complement event: The complement of this event is 'randomly choosing a car with one or no cause for showing its "CHECK ENGINE" light.'

Write the mathematical representation: Let P(A) represent the probability of choosing a car with more than one cause for showing its "CHECK ENGINE" light. The complement probability is represented as P(A') = 1 - P(A).

Express the statement clearly: The complement probability is the likelihood of randomly choosing a car with one or no cause for showing its "CHECK ENGINE" light, which is calculated as 1 minus the probability of choosing a car with more than one cause.

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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 the event cannot happen, while a probability of 1 indicates certainty. In this context, it refers to the chance of selecting a car with specific characteristics from a defined population.

Complement of Probability

The complement of a probability event is the probability that the event does not occur. It is calculated as 1 minus the probability of the event. For example, if the probability of choosing a car with more than one cause for the 'CHECK ENGINE' light is P, then the complement would be 1 - P, representing the probability of choosing a car without that characteristic.

Population and Sample

In statistics, a population refers to the entire group of individuals or items that we are interested in studying, while a sample is a subset of that population. In this question, the population consists of all vehicles showing 'CHECK ENGINE' lights, and understanding this distinction is crucial for accurately interpreting probabilities related to specific characteristics within that group.

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Writing In Exercises 89 and 90, write a statement that represents the complement of the probability.90. The probability of randomly choosing a car with more than one cause for showing its "CHECK ENGINE" light from the population of vehicles showing "CHECK ENGINE" lights.