/*! 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} Q118SE Which events are independent?聽U... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q118SE (page 207)

Which events are independent?Use your intuitive understanding of independence to form an opinion about whether each of the following scenarios represents independent events.

a.The results of consecutive tosses of a coin.

b.The opinions of randomly selected individuals in a pre-election poll.

c.A Major League Baseball player's results in two consecutive at-bats.

d.The amount of gain or loss associated with investments in different stocks if these stocks are bought on the same day and sold on the same day 1 month later.

e.The amount of gain or loss associated with investments in different stocks bought and sold in different time periods, 5 years apart.

f.The prices bid by two different development firms in response to a building construction proposal.

Short Answer

Expert verified
  1. Event A is independent.
  2. Event B is independent.
  3. Event C is independent.
  4. Event D is not independent.
  5. Event E is independent.
  6. The event F is not independent.

Step by step solution

01

(a) The results of consecutive tosses of a coin

To the data, some flip of a coin does not produce another flip of a coin event. So, event A is independent.

02

(b) The opinions of randomly selected individuals in a pre-election poll

Based on the facts, the view of a randomly picked person together in a pre-election study probably does not impact someone person's current view. Hence, event B is independent.

03

(c) A Major League Baseball player's results in two consecutive at-bats

A. To data, the result of such discussion does not affect something else's occurrence. Accordingly, event C is independent.

04

(d) The amount of gain or loss associated with investments in different stocks if these stocks are bought on the same day and sold on the same day 1 month later

A. To data because of this the earnings or losses in respect of investments in various equities purchased the same day. They offered one month ago and are expected to be substantially connected. Hence, event D is not independent.

05

(e) The amount of gain or loss associated with investments in different stocks that are bought and sold in different time periods, 5 years apart

A. To the data, because occurrences eventuate 5 years separately that is improbable that some stock's bought and sold will influence the purchase and offer from another firm. So, event E is independent.

06

(f) The prices bid by two different development firms in response to a building construction proposal

Since each developer as the data cannot decide the proposition. So, the event F is not independent. Therefore, event F is not independent.

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!

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

Speeding linked to fatal car crashes. According to the National Highway Traffic and Safety Administration鈥檚 National Center for Statistics and Analysis (NCSA), 鈥淪peeding is one of the most prevalent factors contributing to fatal traffic crashes鈥� (NHTSA Technical Report, August 2005). The probability that speeding is a cause of a fatal crash is .3. Furthermore, the probability that speeding and missing a curve are causes of a fatal crash is .12. Given speeding is a cause of a fatal crash, what is the probability that the crash occurred on a curve?

Two fair coins are tossed, and the following events are defined:

A: [Observe one head and one tail.]

B: [Observe at least one head.]

a. Define the possible sample points and assign probabilities to each.

b. Draw a Venn diagram for the experiment, showing the sample points and events A and B.

c. Find P(A), P(B) andP(A鈭�B).

d. Use the formula for conditional probability to find P (A/B)and P (B/A). Verify your answer by inspecting the Venn diagram and using the concept of reduced sample spaces.

Detecting traces of TNT.University of Florida researchersin the Department of Materials Science and Engineering have invented a technique to rapidly detect traces of TNT (Today, Spring 2005). The method, which involves shining a laser light on a potentially contaminated object, provides instantaneous results and gives no false positives. In this application, a false positive would occur if the laser light detects traces of TNT when, in fact, no TNT is actually present on the object. Let A be the event that the laser light detects traces of TNT. Let B be the event that the object contains no traces of TNT. The probability of a false positive is 0. Write this probability in terms of A and B using symbols such as鈭�,鈭�and |.

Guilt in decision making.Refer to the Journal of Behavioral Decision Making(January 2007) study of theeffect of guilt emotion on how a decision maker focuseson a problem, Exercise 3.48 (p. 183). The results (numberresponding in each category) for the 171 study participantsare reproduced in the table below. Suppose one of the 171participants is selected at random.

Emotional

State

Choose

Stated Option

Do Not Choose

Stated Option

Totals

Guilt

Anger

Neutral

45

8

7

12

50

49

57

58

56

Totals

60

111

171

a.Given that the respondent is assigned to the guilty state, what is the probability that the respondent chooses the stated option?

b.If the respondent does not choose to repair the car, what is the probability that the respondent is in the anger state?

c.Are the events {repair the car} and {guilty state }
independent?

Which of the following pairs of events are mutually exclusive? Justify your response.

  1. {The next customer entering a retail store is older than 30 years.}, {The next customer entering the same retail store is younger than 20 years.}
  2. {The next customer entering a retail store is younger than 20 years.}, {The next customer entering the same retail store will spend more than \(900 in purchases.}
  3. {The next customer entering the retail store will be older than 70 years and spend more than \)900 in purchases.}, {The next customer entering the same retail store will try to steal an item.}
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision 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.