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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 is expressed as a percentage: 25%.
02

Understand the Percentage

Percentages are based on a scale from 0 to 100. A percentage can be converted to a decimal value between 0 and 1 by dividing by 100.
03

Convert the Percentage to a Decimal

Convert 25% to a decimal by dividing 25 by 100: 25/100 = 0.25.
04

Express the Probability as a Decimal

The probability of rain today expressed as a value between 0 and 1 is 0.25.

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Key Concepts

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

probability
Probability is the measure of how likely an event is to occur. It is a value that can range from 0 to 1, where 0 indicates the event is impossible, and 1 indicates the event is certain to happen. When we say the probability of an event is 0.25, it means there is a 25% chance of that event occurring. Understanding probability helps in making predictions based on known data. For example, if meteorologists say there is a 25% chance of rain, you can use this to prepare accordingly.
percentage conversion
Percentages are a way to express numbers as parts of a whole, specifically out of 100. To convert a percentage to a probability (or a decimal value between 0 and 1), we need to divide by 100. For instance, converting 25% to a probability involves this simple calculation:
  • Take the percentage value (25%).
  • Divide by 100.
  • This gives us 25/100 = 0.25.
By converting percentages to decimals, it simplifies comparisons and calculations in various applications, such as statistics, finance, and probability.
decimals
Decimals are a way to represent fractions and are used extensively in mathematics. They are a numerical representation that shows parts of a whole as values between whole numbers. In the context of probability, decimals make it easy to see and understand the likelihood of an event. For example, the decimal 0.25 represents 25%, or 25 out of 100 parts. To convert a fraction to a decimal, you simply divide the numerator by the denominator. For instance, to find the decimal representation of 25/100:
  • Perform the division: 25 梅 100.
  • The result is 0.25.
Therefore, expressing probability in decimal form allows for more straightforward mathematical operations and comparisons.

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Most popular questions from this chapter

Express all probabilities as fractions. In a horse race, a quinela bet is won if you selected the two horses that finish first and second, and they can be selected in any order. The 140 th running of the Kentucky Derby had a field of 19 horses. What is the probability of winning a quinela bet if random horse selections are made?

\(The symbol ! is the factorial symbol that represents the product of decreasing whole numbers, as in 6! = 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2\cdot 1 = 720. Six people can stand in line 720 different ways.\)

a. Five 鈥渕athletes鈥� celebrate after solving a particularly challenging problem during competition. If each mathlete high fives each other mathlete exactly once, what is the total number of high fives? b. If n mathletes shake hands with each other exactly once, what is the total number of handshakes? c. How many different ways can five mathletes be seated at a round table? (Assume that if everyone moves to the right, the seating arrangement is the same.) d. How many different ways can n mathletes be seated at a round table?

Express all probabilities as fractions. A classic counting problem is to determine the number of different ways that the letters of "Mississippi" can be arranged. Find that number.

In Exercises 29 and \(30,\) find the probabilities and indicate when the "5\% guideline for cumbersome calculations" is used. Medical Helicopters In a study of helicopter usage and patient survival, results were obtained from 47,637 patients transported by helicopter and 111,874 patients transported by ground (based on data from "Association Between Helicopter vs Ground Emergency Medical Services and Survival for Adults with Major Trauma," by Galvagno et al., Journal of the American Medical Association, Vol. 307, No. 15). a. If 1 of the 159,511 patients in the study is randomly selected, what is the probability that the subject was transported by helicopter? b. If 5 of the subjects in the study are randomly selected without replacement, what is the probability that all of them were transported by helicopter?
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