/*! 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 18 Explain why the statement is inc... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 18

Explain why the statement is incorrect. The probability that a certain stock will increase in value over a period of 1 week is .6. Therefore, the probability that the stock will decrease in value is \(.4\).

Short Answer

Expert verified
The statement "The probability that a certain stock will increase in value over a period of 1 week is .6. Therefore, the probability that the stock will decrease in value is \(.4\)." is not necessarily incorrect as it follows the probability rule when considering only two possible outcomes (stock increasing or decreasing). However, it might be incomplete and incorrect if there is a third possible outcome, such as the stock value remaining constant. The correctness of the statement depends on whether there are more possible outcomes and their respective probabilities. More information is needed to thoroughly verify the statement.

Step by step solution

01

Identify the Given Statement

The given statement is "The probability that a certain stock will increase in value over a period of 1 week is .6. Therefore, the probability that the stock will decrease in value is \(.4\)."
02

Review Probability Concepts

In probability theory, the probability of an event A happening is given by P(A). The probability of the complementary event, A not happening (denoted by A'), is given by P(A'). The sum of the probabilities of an event and its complementary event is always equal to 1. Mathematically, this is expressed as follows: P(A) + P(A') = 1.
03

Analyze the Given Probabilities

According to the statement, the probability of a certain stock increasing in value over a period of 1 week is 0.6 (P(stock increasing) = 0.6). It is assumed that the stock decreasing in value is the complementary event to the stock increasing in value. Using the probability rule, the probability of the stock decreasing in value should be: P(stock decreasing) = 1 - P(stock increasing) = 1 - 0.6 = 0.4.
04

Determine if the Statement is Incorrect

Based on the probability concepts and our calculation, the statement "The probability that a certain stock will increase in value over a period of 1 week is .6. Therefore, the probability that the stock will decrease in value is \(.4\)." appears to be correct. The probability of the stock decreasing in value is indeed 0.4 when the probability of the stock increasing in value is 0.6, as calculated using the probability rule. Although the statement seems to be correct when considering only these two possible outcomes (stock increasing or decreasing in value), it's important to remember that there might be a third scenario, i.e., the stock value remains constant. If this is the case, the given statement would be incomplete and incorrect, as it does not account for the probability of the stock remaining constant. Therefore, to thoroughly verify the correctness of the statement, we would need more information about the possible outcomes and their respective probabilities.

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.

Complementary Events
In probability theory, complementary events are two outcomes that cannot happen at the same time. If one event occurs, the other cannot. For example, when flipping a coin, the events of getting heads and not getting heads (which means tails) are complementary.

The probabilities of complementary events add up to 1. This simple rule can be expressed mathematically:
  • Let P(A) be the probability of event A occurring.
  • Then, the probability of the complementary event A' is P(A') = 1 - P(A).
Using this formula helps you find the probability of the complementary event if you know the probability of the initial event.
Probability of Outcomes
When discussing the probability of outcomes, it's crucial to recognize all possible scenarios. In the example from the exercise, it's given that the probability of a stock increasing is 0.6. By assuming this is one of two outcomes, the other being the stock decreasing, the statement seems correct using:
  • P(stock increasing) = 0.6
  • P(stock decreasing) = 1 - P(stock increasing) = 0.4
However, this explanation doesn't consider if the stock price could stay unchanged, which is a third possible outcome. Therefore, simply splitting outcomes into increasing or decreasing might not account for all possibilities.

The probability of outcomes should cover all potential scenarios to be accurate in the analysis of real-world situations like stock market fluctuations.
Stock Market Probabilities
The stock market is known for its volatility and complexity. This means that predicting whether a stock will go up, down, or stay the same involves assessing multiple factors. It is tempting to simplify the probabilities into binary outcomes (up or down), but real stock behavior can include price stability.

Accurately calculating stock market probabilities requires understanding:
  • Historical performance and trends.
  • Current market conditions and economic indicators.
  • Company-specific information and news.
  • Potential for unexpected events affecting value.
Remembering that "up," "down," or "unchanged" are all possibilities can lead to more accurate models and decision-making in financial analysis.

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

A nationwide survey conducted by the National Cancer Society revealed the following information. Of 10,000 people surveyed, 3200 were "heavy coffee drinkers" and 160 had cancer of the pancreas. Of those who had cancer of the pancreas, 132 were heavy coffee drinkers. Using the data in this survey, determine whether the events "being a heavy coffee drinker" and "having cancer of the pancreas" are independent events.

In a three-child family, what is the probability that all three children are girls given that at least one of the children is a girl? (Assume that the probability of a boy being born is the same as the probability of a girl being born.)

There were 80 male guests at a party. The number of men in each of four age categories is given in the following table. The table also gives the probability that a man in the respective age category will keep his paper money in order of denomination. $$\begin{array}{lcc} \hline \text { Age } & \text { Men } & \text { Keep Paper Money in Order, \% } \\\ \hline 21-34 & 25 & 9 \\ \hline 35-44 & 30 & 61 \\ \hline 45-54 & 15 & 80 \\ \hline 55 \text { and over } & 10 & 80 \\ \hline \end{array}$$ A man's wallet was retrieved and the paper money in it was kept in order of denomination. What is the probability that the wallet belonged to a male guest between the ages of 35 and 44 ?

Propuct Reuasiumr The proprietor of Cunningham's Hardware Store has decided to install floodlights on the premises as a measure against vandalism and theft. If the probability is \(.01\) that a certain brand of floodlight will burn out within a year, find the minimum number of floodlights that must be installed to ensure that the probability that at least one of them will remain functional for the whole year is at least .99999. (Assume that the floodlights operate independently.)

In "The Numbers Game," a state lottery, four numbers are drawn with replacement from an urn containing balls numbered \(0-9\), inclusive. Find the probability that a ticket holder has the indicated winning ticket. Three digits in exact order
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.