/*! 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 5 A jar contains four coins: a nic... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 5

A jar contains four coins: a nickel, a dime, a quarter, and a half-dollar. Three coins are randomly selected from the jar. a. List the simple events in \(S\). b. What is the probability that the selection will contain the half-dollar? c. What is the probability that the total amount drawn will equal \(60 \phi\) or more?

Short Answer

Expert verified
Answer: The probability of selecting a half-dollar coin is 3/4, and the probability of having a total amount of 60 cents or more is also 3/4.

Step by step solution

01

List the simple events in the \(S\)

To find all possible simple events, we will list all the possible combinations of selecting three coins from the jar. The simple events can be represented as ordered triples, \((N, D, Q, H)\) where \(N, D, Q, H\) stand for a nickel, dime, quarter, and half-dollar respectively. The sample space \(S\) contains all outcomes of selecting three coins: \(S=\{(N,D,Q), (N,D,H), (N,Q,H), (D,Q,H)\}\)
02

Find the probability of the half-dollar being in the selection

To find the probability of the half-dollar being in the selection, we will simply count the number of simple events that include the half-dollar and divide by the total number of simple events in \(S\). Out of the four simple events, three of them have the half-dollar in their selection, so the probability is: \(P(H) = \frac{3}{4}\)
03

Calculate the total amount for each simple event

To find the probability of having a total amount of \(60\phi\) cents or more, we will first need to calculate the total amount for each simple event: 1. \((N,D,Q)\): The total sum is \(5 + 10 + 25 = 40\phi\) cents. 2. \((N,D,H)\): The total sum is \(5 + 10 + 50 = 65\phi\) cents. 3. \((N,Q,H)\): The total sum is \(5 + 25 + 50 = 80\phi\) cents. 4. \((D,Q,H)\): The total sum is \(10 + 25 + 50 = 85\phi\) cents.
04

Calculate the probability of having a total amount of \(60\phi\) cents or more

Now we can find the probability of having a total amount of \(60\phi\) cents or more by counting the number of simple events that meet this condition and dividing by the total number of simple events: There are 3 out of 4 simple events that meet this condition, so the probability is: \(P(60\phi\text{ cents or more}) = \frac{3}{4}\)

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

Suppose that a certain disease is present in \(10 \%\) of the population, and that there is a screening test designed to detect this disease if present. The test does not always work perfectly. Sometimes the test is negative when the disease is present, and sometimes it is positive when the disease is absent. The table below shows the proportion of times that the test produces various results. a. Find the following probabilities from the table: \(P(D), P\left(D^{c}\right), P\left(N \mid D^{c}\right), P(N \mid D)\) b. Use Bayes' Rule and the results of part a to find \(P(D \mid N)\) c. Use the definition of conditional probability to find \(P(D \mid N)\). (Your answer should be the same as the answer to part b.) d. Find the probability of a false positive, that the test is positive, given that the person is disease-free. e. Find the probability of a false negative, that the test is negative, given that the person has the disease. f. Are either of the probabilities in parts \(\mathrm{d}\) or e large enough that you would be concerned about the reliability of this screening method? Explain.

Refer to Exercise 4.14, in which a 100 -meter sprint is run by John, Bill, Ed, and Dave. Assume that all of the runners are equally qualified, so that any order of finish is equally likely. Use the \(m n\) Rule or permutations to answer these questions: a. How many orders of finish are possible? b. What is the probability that Dave wins the sprint? c. What is the probability that Dave wins and John places second? d. What is the probability that Ed finishes last?

From experience, a shipping company knows that the cost of delivering a small package within 24 hours is \(\$ 14.80 .\) The company charges \(\$ 15.50\) for shipment but guarantees to refund the charge if delivery is not made within 24 hours. If the company fails to deliver only \(2 \%\) of its packages within the 24 -hour period, what is the expected gain per package?

An experiment can result in one of five equally likely simple events, \(E_{1}, E_{2}, \ldots, E_{5} .\) Events \(A, B,\) and \(C\) are defined as follows: $$A: E_{1}, E_{3} \quad P(A)=.4$$ $$B: E_{1}, E_{2}, E_{4}, E_{5} \quad P(B)=.8$$ $$C: E_{3}, E_{4} \quad P(C)=.4$$. Find the probabilities associated with these compound events by listing the simple events in each. a. \(A^{c}\) b. \(A \cap B\) c. \(B \cap C\) d. \(A \cup B\) e. \(B \mid C\) f. \(A \mid B\) g. \(A \cup B \cup C\) h. \((A \cap B)^{c}\)

A random variable \(x\) has this probability distribution: $$\begin{array}{l|rrrrrr}x & 0 & 1 & 2 & 3 & 4 & 5 \\\\\hline p(x) & .1 & .3 & .4 & .1 & ? & .05\end{array}$$ a. Find \(p(4)\). b. Construct a probability histogram to describe \(p(x)\). c. Find \(\mu, \sigma^{2},\) and \(\sigma\). d. Locate the interval \(\mu \pm 2 \sigma\) on the \(x\) -axis of the histogram. What is the probability that \(x\) will fall into this interval? e. If you were to select a very large number of values of \(x\) from the population, would most fall into the interval \(\mu \pm 2 \sigma ?\) Explain.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.