/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 33 The probability of winning the g... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 33

The probability of winning the grand prize at a particular carnival game is 0.005. Is the outcome of winning very likely or very unlikely?

Short Answer

Expert verified
Winning the grand prize is very unlikely, with a probability of 0.005.

Step by step solution

01

Understanding the Probability Scale

Probabilities range from 0 to 1, where 0 indicates an impossible event and 1 indicates a certain event. A probability closer to 0 suggests that an event is very unlikely, whereas a probability closer to 1 suggests that an event is very likely.
02

Interpreting Small Probabilities

A probability of 0.005 is quite small, meaning it is very close to 0 on the probability scale. This indicates that the occurrence of this event (winning the grand prize) is not very likely and is, in fact, quite rare.
03

Comparing to Thresholds

Typically, events with probabilities less than 0.05 (or 5%) are considered statistically rare or unlikely. Since 0.005 is much less than 0.05, it reinforces the conclusion that winning is very unlikely.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Probability Scale
Understanding the probability scale is essential when working with probabilities, as it helps you to determine how likely an event is to occur. The scale ranges from 0 to 1. A probability of 0 means that an event is impossible, like trying to roll a 7 on a standard six-sided die.
On the other hand, a probability of 1 means an event is certain, like the sun rising in the east.
Most probabilities fall somewhere between these two extremes.
  • A probability closer to 0 indicates that an event is less likely to occur, or unlikely.
  • A probability closer to 1 indicates that an event is more likely to happen, or likely.
  • A probability of 0.5 implies an event is equally likely to happen as not happen, like flipping a fair coin and getting heads.
The scale is useful for visualizing and comparing the likelihood of different events. This helps you make informed decisions based on how probable an event is estimated to be.
Event Likelihood
The likelihood of an event occurring can be thought of as the chance or probability of its occurrence. To determine if an event is likely or unlikely, compare its probability to established thresholds.

For example:
  • A probability less than 0.05 is generally considered rare or unlikely.
  • A probability between 0.05 and 0.5 is considered possible but not guaranteed.
  • A probability greater than 0.5 and less than 1 suggests an event is likely but not certain.
In the context of the given probability of 0.005, it is evident this is a rare occurrence since it is far less than 0.05. Therefore, it implies that winning the grand prize in the carnival game is very unlikely.
Interpreting Probabilities
Interpreting probabilities involves understanding what a given probability means in terms of real-world expected outcomes. It is crucial for making predictions and informed decisions.

A few tips for successfully interpreting probabilities are:
  • Recognize that probabilities provide a number of how often an event is expected to occur in a large number of trials.
  • Remember that a small probability indicates the event might happen sometimes, but not often.
  • Understand that probabilities near 0.5 mean an event is as likely to happen as not.
  • Compare the probability to known thresholds to assess the rarity or likelihood of an event, such as using 0.05 or 5% when determining if something is rare.
By interpreting the probability of 0.005, one can conclude that an event, like winning a carnival game, is exceptionally rare and unlikely to occur often, if at all. Proper interpretation helps in setting realistic expectations about outcomes.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Which distribution do you use when you are testing a population mean and the standard deviation is known? Assume sample size is large.

"Dalmatian Darnation," by Kathy Sparling A greedy dog breeder named Spreckles Bred puppies with numerous freckles The Dalmatians he sought Possessed spot upon spot The more spots, he thought, the more shekels. His competitors did not agree That freckles would increase the fee. They said, 鈥淪pots are quite nice But they don't affect price; One should breed for improved pedigree.鈥� The breeders decided to prove This strategy was a wrong move. Breeding only for spots Would wreak havoc, they thought. His theory they want to disprove. They proposed a contest to Spreckles Comparing dog prices to freckles. In records they looked up One hundred one pups: Dalmatians that fetched the most shekels. They asked Mr. Spreckles to name An average spot count he'd claim To bring in big bucks. Said Spreckles, 鈥淲ell, shucks, It's for one hundred one that I aim.鈥� Said an amateur statistician Who wanted to help with this mission. 鈥淭wenty-one for the sample Standard deviation's ample: They examined one hundred and one Dalmatians that fetched a good sum. They counted each spot, Mark, freckle and dot And tallied up every one. Instead of one hundred one spots They averaged ninety six dots Can they muzzle Spreckles鈥� Obsession with freckles Based on all the dog data they've got?

The mean age of graduate students at a University is at most 31 y ears with a standard deviation of two years. A random sample of 15 graduate students is taken. The sample mean is 32 years and the sample standard deviation is three years. Are the data significant at the 1\(\%\) level? The p-value is \(0.0264 .\) State the null and alternative hypotheses and interpret the \(p\) -value.

Assume \(H_{0} : p=0.25\) and \(H a : p \neq 0.25 .\) Is this a left-tailed, right-tailed, or two-tailed test?

In a population of fish, approximately 42% are female. A test is conducted to see if, in fact, the proportion is less. State the null and alternative hypotheses.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.