In Exercises 13–20, express the indicated degree of likelihood as...

4. Probability

Basic Concepts of Probability

Statistics

4. Probability

Basic Concepts of Probability

1:27 minutes

Problem 4.1.17

Textbook Question

In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1.

Randomness When using a computer to randomly generate the last digit of a phone number to be called for a survey, there is 1 chance in 10 that the last digit is zero

Verified step by step guidance

Understand the problem: The likelihood of an event is expressed as a probability, which is a value between 0 and 1. Here, the event is the last digit of a phone number being zero, and the given likelihood is '1 chance in 10.'

Recall the formula for probability: \( P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \).

Identify the favorable outcomes: In this case, the favorable outcome is the last digit being zero, which is 1 outcome.

Identify the total possible outcomes: Since the last digit of a phone number can be any digit from 0 to 9, there are 10 possible outcomes in total.

Substitute the values into the formula: \( P(E) = \frac{1}{10} \). This fraction represents the probability of the last digit being zero.

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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 value between 0 and 1. A probability of 0 indicates that the event cannot happen, while a probability of 1 indicates certainty that the event will occur. In this context, the probability of the last digit being zero is calculated based on the total number of possible outcomes.

Randomness

Randomness refers to the lack of pattern or predictability in events. In statistical terms, a random process produces outcomes that are not influenced by previous outcomes. When generating the last digit of a phone number randomly, each digit from 0 to 9 has an equal chance of being selected, ensuring that the selection is unbiased and truly random.

Sample Space

The sample space is the set of all possible outcomes of a random experiment. For the last digit of a phone number, the sample space consists of the digits 0 through 9, totaling 10 possible outcomes. Understanding the sample space is crucial for calculating probabilities, as it provides the basis for determining the likelihood of specific events occurring within that space.

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In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1.Randomness When using a computer to randomly generate the last digit of a phone number to be called for a survey, there is 1 chance in 10 that the last digit is zero