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Chapter 5: Problem 11

Which of the following numbers could be the probability of an event? $$ 0,0.01,0.35,-0.4,1,1.4 $$

Short Answer

Expert verified
The valid probabilities are 0, 0.01, 0.35, and 1.

Step by step solution

01

Understand the Range of Probability

Recall that probability values must lie within the range [0, 1]. This means a valid probability value cannot be less than 0 or greater than 1.
02

Evaluate Each Given Number

Assess each number given in the list:- \(0\): This is within the range [0, 1].- \(0.01\): This is within the range [0, 1].- \(0.35\): This is within the range [0, 1].- \(-0.4\): This number is less than 0, so it is not a valid probability.- \(1\): This is within the range [0, 1].- \(1.4\): This number is greater than 1, so it is not a valid probability.
03

List the Valid Probabilities

List out the numbers that fall within the valid range. These are: 0, 0.01, 0.35, and 1.

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Key Concepts

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

range of probability
The range of probability is crucial to understand when dealing with probability problems. Probability values are numbers that represent the chance or likelihood of an event occurring. These values always lie within a specific range.
Probabilities can only fall between 0 and 1, inclusive.
This means the smallest probability value is 0 (indicating an impossible event), and the largest is 1 (indicating a certain event).
Any number outside this range cannot represent a valid probability. For example, a probability of -0.4 or 1.4 is not valid because they are outside the allowed range from 0 to 1.
valid probability values
Determining valid probability values requires ensuring that the numbers fall within the range [0, 1].
Let's assess whether each number in the list could be a probability:
  • de0: This value is within the range [0, 1].
  • 0.01: This is also within the range [0, 1].
  • 0.35: Again, this falls within the range [0, 1].
  • -0.4: This value is less than 0, making it an invalid probability.
  • 1: This value is equal to 1, thus within the range [0, 1].
  • 1.4: Since this value is greater than 1, it is not valid.

From this, the valid probability values are 0, 0.01, 0.35, and 1. Each of these lies within the specified range.
probability assessment
Probability assessment is the process of evaluating numbers to determine if they can be valid probabilities.
Follow these steps to assess if a given value can be a probability:
  • Check if the number is within the range [0, 1].
  • If it is, the number is a valid probability.
  • If it isn't, the number is not a valid probability.

For the list provided, we've identified the valid probabilities through this process: 0, 0.01, 0.35, and 1.
Confidence in probability assessments helps in accurately analyzing situations and foretelling the likelihood of occurrences.
Remember to always stay within the bounds of the probability range when performing these evaluations!

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Most popular questions from this chapter

A flush in the card game of poker occurs if a player gets five cards that are all the same suit (clubs, diamonds, hearts, or spades). Answer the following questions to obtain the probability of being dealt a flush in five cards. (a) We initially concentrate on one suit, say clubs. There are 13 clubs in a deck. Compute \(P(\) five clubs \()=P(\) first card is clubs and second card is clubs and third card is clubs and fourth card is clubs and fifth card is clubs). (b) A flush can occur if we get five clubs or five diamonds or five hearts or five spades. Compute \(P\) (five clubs or five diamonds or five hearts or five spades). Note that the events are mutually exclusive.

You are planning a trip to a water park tomorrow and the weather forecaster says there is a \(70 \%\) chance of rain. Explain what this result means.

What is the probability of an event that is impossible? Suppose that a probability is approximated to be zero based on empirical results. Does this mean the event is impossible?

Adult Americans (18 years or older) were asked whether they used social media (Facebook, Twitter, and so on ) regularly. The following table is based on the results of the survey. $$ \begin{array}{lccccc} & \mathbf{1 8 - 3 4} & \mathbf{3 5 - 4 4} & \mathbf{4 5 - 5 4} & \mathbf{5 5 +} & \text { Total } \\ \hline \begin{array}{l} \text { Use social } \\ \text { media } \end{array} & 117 & 89 & 83 & 49 & \mathbf{3 3 8} \\ \hline \begin{array}{l} \text { Do not use } \\ \text { social media } \end{array} & 33 & 36 & 57 & 66 & \mathbf{1 9 2} \\ \hline \text { Total } & \mathbf{1 5 0} & \mathbf{1 2 5} & \mathbf{1 4 0} & \mathbf{1 1 5} & \mathbf{5 3 0} \\ \hline \end{array} $$ (a) What is the probability that a randomly selected adult American uses social media, given the individual is \(18-34\) years of age? (b) What is the probability that a randomly selected adult American is \(18-34\) years of age, given the individual uses social media? (c) Are 18 - to 34 -year olds more likely to use social media than individuals in general? Why?

Describe what an unusual event is. Should the same cutoff always be used to identify unusual events? Why or why not?
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