/*! 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 3 True or False: In a probability ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 3

True or False: In a probability model, the sum of the probabilities of all outcomes must equal 1 .

Short Answer

Expert verified
True. The sum of probabilities of all outcomes in a probability model must equal 1.

Step by step solution

01

Understanding Probability Models

A probability model is a mathematical representation of a random phenomenon. It includes all possible outcomes of the phenomenon and the probabilities associated with these outcomes.
02

Sum of Probabilities

In any probability model, the total probability of all possible outcomes must add up to 1. This is because the probability of one of the outcomes occurring is certain (i.e., 100%), which is represented as 1 in probability terms.
03

Evaluating the Statement

The statement says: 'In a probability model, the sum of the probabilities of all outcomes must equal 1.' Since the definition of a probability model requires the sum of the probabilities of all possible outcomes to be 1, this statement is indeed true.

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 Theory
Probability theory is a mathematical framework for quantifying uncertainty. It helps us understand the likelihood of different outcomes in random events.
  • One key aspect is the concept of probability, which is a numerical measure ranging from 0 (impossible event) to 1 (certain event).
  • In probability theory, events are often modeled using a probability space, comprising a sample space (all possible outcomes), events (specific subsets of outcomes), and a probability function that assigns probabilities to these events.
Understanding probability theory is crucial for analyzing random phenomena, making decisions, and predicting future events based on statistical interpretations.
Sum of Probabilities
In any probability model, the sum of the probabilities of all possible outcomes must be 1. This is a fundamental rule of probability theory. Here's why:
  • When we list all possible outcomes of a random phenomenon, these outcomes must cover every possible event in the sample space.
  • Each individual outcome has a probability assigned to it, representing the likelihood of that outcome occurring.
  • If you add up the probabilities of all possible outcomes, you get a total probability of 1, which means one of the outcomes is certain to occur.
This principle ensures that the total probability distribution is complete and accounts for every possible scenario.
Random Phenomenon
A random phenomenon is any situation where the outcome is uncertain until it occurs. These phenomena are unpredictable on an individual trial basis but exhibit regular patterns over many trials.
They are characterized by:
  • Uncertainty in individual outcomes: Each event cannot be precisely predicted before it happens.
  • Predictable patterns in the long run: While single events are unpredictable, the overall distribution of many events can show a clear pattern.
  • Examples: Tossing a coin, rolling a die, and lottery drawings are all random phenomena.
By studying these phenomena through probability models, we can better understand and predict their behavior over time.

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

Birthdays Exclude leap years from the following calculations and assume each birthday is equally likely: (a) Determine the probability that a randomly selected person has a birthday on the 1 st day of a month. Interpret this probability. (b) Determine the probability that a randomly selected person has a birthday on the 31 st day of a month. Interpret this probability. (c) Determine the probability that a randomly selected person was born in December. Interpret this probability. (d) Determine the probability that a randomly selected person has a birthday on November 8 . Interpret this probability. (e) If you just met somebody and she asked you to guess her birthday, are you likely to be correct? (f) Do you think it is appropriate to use the methods of classical probability to compute the probability that a person is born in December?

Suppose that you roll a pair of dice 1000 times and get seven 350 times. Based on these results, what is the probability that the next roll results in seven?

Because of a manufacturing error, three cans of regular soda were accidentally filled with diet soda and placed into a 12 -pack. Suppose that two cans are randomly selected from the 12 -pack. (a) Determine the probability that both contain diet soda. (b) Determine the probability that both contain regular soda. Would this be unusual? (c) Determine the probability that exactly one is diet and one is regular?

Why is the following not a probability model? $$ \begin{array}{lc} \text { Color } & \text { Probability } \\ \hline \text { Red } & 0.3 \\ \hline \text { Green } & -0.3 \\ \hline \text { Blue } & 0.2 \\ \hline \text { Brown } & 0.4 \\ \hline \text { Yellow } & 0.2 \\ \hline \text { Orange } & 0.2 \\ \hline \end{array} $$

A bag of 30 tulip bulbs purchased from a nursery contains 12 red tulip bulbs, 10 yellow tulip bulbs, and 8 purple tulip bulbs. Use a tree diagram like the one in Example 5 to answer the following: (a) What is the probability that two randomly selected tulip bulbs are both red? (b) What is the probability that the first bulb selected is red and the second yellow? (c) What is the probability that the first bulb selected is yellow and the second is red? (d) What is the probability that one bulb is red and the other yellow?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Calculus

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.