/*! 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

Lingo In the gameshow Lingo, the team that correctly guesses a mystery word gets a chance to pull two Lingo balls from a bin. Balls in the bin are labeled with numbers corresponding to the numbers remaining on their Lingo board. There are also three prize balls and three red "stopper" balls in the bin. If a stopper ball is drawn first, the team loses their second draw. To form a Lingo, the team needs five numbers in a vertical, horizontal, or diagonal row. Consider the sample Lingo board below for a team that has just guessed a mystery word. $$ \begin{array}{|l|l|l|l|l|} \hline \mathbf{L} & \mathbf{I} & \mathbf{N} & \mathbf{G} & \mathbf{O} \\ \hline 10 & & & 48 & 66 \\ \hline & & 34 & & 74 \\ \hline & & 22 & 58 & 68 \\ \hline 4 & 16 & & 40 & 70 \\ \hline & 26 & 52 & & 64 \\ \hline \end{array} $$ (a) What is the probability that the first ball selected is on the Lingo board? (b) What is the probability that the team draws a stopper ball on its first draw? (c) What is the probability that the team makes a Lingo on their first draw? (d) What is the probability that the team makes a Lingo on their second draw?

Suppose that Ralph gets a strike when bowling \(30 \%\) of the time. (a) What is the probability that Ralph gets two strikes in a row? (b) What is the probability that Ralph gets a turkey (three strikes in a row)? (c) When events are independent, their complements are independent as well. Use this result to determine the probability that Ralph gets a turkey, but fails to get a clover (four strikes in a row).

In 2002, Valerie Wilson won \(\$ 1\) million in a scratch-off game (Cool Million) from the New York lottery. Four years later, she won \(\$ 1\) million in another scratch-off game \((\$ 3,000,000\) Jubilee \(),\) becoming the first person in New York state lottery history to win \(\$ 1\) million or more in a scratch-off game twice. In the first game, she beat odds of 1 in 5.2 million to win. In the second, she beat odds of 1 in 705,600 . (a) What is the probability that an individual would win \(\$ 1\) million in both games if they bought one scratch-off ticket from each game? (b) What is the probability that an individual would win \(\$ 1\) million twice in the \(\$ 3,000,000\) Jubilee scratch-off game?

A golf-course architect has four linden trees, five white birch trees, and two bald cypress trees to plant in a row along a fairway. In how many ways can the landscaper plant the trees in a row, assuming that the trees are evenly spaced?

The probability that a randomly selected 40-year-old female will live to be 41 years old is 0.99855 according to the National Vital Statistics Report, Vol. 56, No. \(9 .\) (a) What is the probability that two randomly selected 40 -yearold females will live to be 41 years old? (b) What is the probability that five randomly selected 40 -yearold females will live to be 41 years old? (c) What is the probability that at least one of five randomly selected 40 -year-old females will not live to be 41 years old? Would it be unusual if at least one of five randomly selected 40-year-old females did not live to be 41 years old?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

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.