/*! 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 9 A survey classified a large numb... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 9

A survey classified a large number of adults according to whether they were judged to need eyeglasses to correct their reading vision and whether they used eyeglasses when reading. The proportions falling into the four categories are shown in the table. (Note that a small proportion, .02, of adults used eyeglasses when in fact they were judged not to need them.) $$\begin{array}{lcc} & \begin{array}{l}\text { Used Eyeglasses } \\\\\text { for Reading }\end{array} \\\\\hline \text { Judged to Need } & & \\ \text { Eyeglasses } & \text { Yes } & \text { No } \\\\\hline \text { Yes } & .44 & .14 \\\\\text { No } & .02 & .40\end{array}$$ If a single adult is selected from this large group, find the probability of each event: a. The adult is judged to need eyeglasses. b. The adult needs eyeglasses for reading but does not use them. c. The adult uses eyeglasses for reading whether he or she needs them or not.

Short Answer

Expert verified
Based on the provided table, the probabilities of each event are as follows: a. The probability of the adult being judged to need eyeglasses (Event A) is P(A) = 0.58. b. The probability of the adult needing eyeglasses but not using them (Event B) is P(B) = 0.14. c. The probability of the adult using eyeglasses for reading whether he or she needs them or not (Event C) is P(C) = 0.46.

Step by step solution

01

Identify cells corresponding to Event A

From the table, the cells corresponding to adults that are judged to need eyeglasses are: "Yes" in the "Judged to Need Eyeglasses" row, and "Yes" and "No" in the "Used Eyeglasses for Reading" column.
02

Calculate the probability of Event A

The probability of Event A can be calculated by adding the proportions in the identified cells: P(A) = 0.44 + 0.14 = 0.58 #b. Probability of the adult needing eyeglasses but not using them# Event B: The adult needs eyeglasses for reading but does not use them.
03

Identify cells corresponding to Event B

From the table, the cells corresponding to adults that need eyeglasses but do not use them are: "Yes" in the "Judged to Need Eyeglasses" row, and "No" in the "Used Eyeglasses for Reading" column.
04

Calculate the probability of Event B

The probability of Event B can be calculated by adding the proportions in the identified cells: P(B) = 0.14 #c. Probability of the adult using eyeglasses for reading whether he or she needs them or not# Event C: The adult uses eyeglasses for reading whether he or she needs them or not.
05

Identify cells corresponding to Event C

From the table, the cells corresponding to adults that use eyeglasses for reading are: "Yes" in the "Used Eyeglasses for Reading" column, and "Yes" and "No" in the "Judged to Need Eyeglasses" row.
06

Calculate the probability of Event C

The probability of Event C can be calculated by adding the proportions in the identified cells: P(C) = 0.44 + 0.02 = 0.46

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

A French restaurant in Riverside, California, offers a special summer menu in which, for a fixed dinner cost, you can choose from one of two salads, one of two entrees, and one of two desserts. How many different dinners are available?

Four union men, two from a minority group, are assigned to four distinctly different one-man jobs, which can be ranked in order of desirability. a. Define the experiment. b. List the simple events in \(S\). c. If the assignment to the jobs is unbiased-that is, if any one ordering of assignments is as probable as any other-what is the probability that the two men from the minority group are assigned to the least desirable jobs?

Past experience has shown that, on the average, only 1 in 10 wells drilled hits oil. Let \(x\) be the number of drillings until the first success (oil is struck). Assume that the drillings represent independent events. a. Find \(p(1), p(2)\), and \(p(3)\). b. Give a formula for \(p(x)\). c. Graph \(p(x)\).

You own 4 pairs of jeans, 12 clean T-shirts, and 4 wearable pairs of sneakers. How many outfits (jeans, T-shirt, and sneakers) can you create?

Gregor Mendel was a monk who suggested in 1865 a theory of inheritance based on the science of genetics. He identified heterozygous individuals for flower color that had two alleles (one \(\mathrm{r}=\) recessive white color allele and one \(\mathrm{R}=\) dominant red color allele). When these individuals were mated, \(3 / 4\) of the offspring were observed to have red flowers and \(1 / 4\) had white flowers. The table summarizes this mating; each parent gives one of its alleles to form the gene of the offspring. We assume that each parent is equally likely to give either of the two alleles and that, if either one or two of the alleles in a pair is dominant (R), the offspring will have red flowers. a. What is the probability that an offspring in this mating has at least one dominant allele? b. What is the probability that an offspring has at least one recessive allele? c. What is the probability that an offspring has one recessive allele, given that the offspring has red flowers?
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Decision Maths

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.