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Chapter 4: Problem 2

Rewrite the following statement so that the likelihood of rain is expressed as a value between 0 and \(1:\) "The probability of rain today is \(25 \%\)."

Short Answer

Expert verified
The probability of rain today is 0.25.

Step by step solution

01

- Identify the Given Probability

The given probability of rain today is stated as a percentage: 25%.
02

- Convert Percentage to Decimal

To express the probability as a value between 0 and 1, convert the percentage to a decimal. To do this, divide the percentage by 100. For example: 25% = \( \frac{25}{100} \)
03

- Perform the Division

Perform the division to get the decimal value: \( \frac{25}{100} = 0.25 \)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

percentages to decimals
Percentages and decimals are two ways of representing the same concept. A percentage is a number out of 100, while a decimal is a number out of 1. Converting a percentage to a decimal can be very handy, especially in probability and statistics. To convert a percentage to a decimal, simply divide the percentage by 100. For example, if you have 25%, divide 25 by 100 which equals 0.25. So, 25% as a decimal is 0.25. This makes it easier to perform mathematical calculations.
probability calculation
Probability is a measure of how likely an event is to occur. It is always a value between 0 and 1. If an event is impossible, its probability is 0. On the other hand, if an event is certain to happen, its probability is 1. To calculate the probability of an event, you divide the number of favorable outcomes by the total number of possible outcomes. For example, if you want to know the probability of getting a heads when flipping a fair coin, you divide the number of ways to get heads (1) by the total number of outcomes (2), which results in 0.5 or 50%.
basic statistics
Statistics is the branch of mathematics that deals with collecting, analyzing, and interpreting data. When dealing with statistics, you often encounter concepts like mean (average), median, and mode. These concepts help summarize large sets of data into understandable numbers. Basic statistics also involve understanding distributions, like the normal distribution, and measures of variability, such as standard deviation. Probability is one of the core principles of statistics and is used to make predictions and informed decisions based on data analysis.

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Most popular questions from this chapter

Find the indicated complements. According to the Bureau of Transportation, \(80.3 \%\) of American Airlines flights arrive on time. What is the probability of randomly selecting an American Airlines flight that does not arrive on time?

Find the probability. It has been reported that \(20 \%\) of iPhones manufactured by Foxconn for a product launch did not meet Apple's quality standards. An engineer needs at least one defective iPhone so she can try to identify the problem(s). If she randomly selects 15 iPhones from a very large batch, what is the probability that she will get at least 1 that is defective? Is that probability high enough so that she can be reasonably sure of getting a defect for her work?

Find the probability and answer the questions. In a recent year in the United States, 83,600 passenger cars rolled over when they crashed, and \(5,127,400\) passenger cars did not roll over when they crashed. Find the probability that a randomly selected passenger car crash results in a rollover. Is it unlikely for a car to roll over in a crash?

Express all probabilities as fractions. The International Morse code is a way of transmitting coded text by using sequences of on \(/\) off tones. Each character is 1 or 2 or 3 or 4 or 5 segments long, and each segment is either a dot or a dash. For example, the letter \(G\) is transmitted as two dashes followed by a dot, as in \(--\bullet\). How many different characters are possible with this scheme? Are there enough characters for the alphabet and numbers?

Use a simulation approach to find the probability that when six consecutive babies are born, there is a run of at least four babies of the same sex. Describe the simulation procedure used, and determine whether such runs are unlikely.
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