Q.127 Use the following information to... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 3: Q.127 (page 232)

Use the following information to answer the next two exercises. The following are real data from Santa Clara County, CA. As of a certain time, there had been a total of $3, 059$ documented cases of AIDS in the county. They were grouped into the following categories:
Suppose a person with AIDS in Santa Clara County is randomly selected.
a. Find P(Person is female).
b. Find P(Person has a risk factor heterosexual contact).
c. Find P(Person is female OR has a risk factor of IV drug user).
d. Find P(Person is female AND has a risk factor of homosexual/bisexual).
e. Find P(Person is male AND has a risk factor of IV drug user).
f. Find P(Person is female GIVEN person got the disease from heterosexual contact).
g. Construct a Venn diagram. Make one group females and the other group heterosexual contact

Short Answer

Expert verified

a. $P (p e r s o n i s f e m a l e) = \frac{255}{3059}$

b. $P (p e r s o n h a s r i s k f a c t o r h e t r o s e x u a l c o n t a c t) = \frac{196}{3059}$

c. $P (P e r s o n i s f e m a l e O R h a s a r i s k f a c t o r o f I V d r u g u s e r) = \frac{788}{3059}$

d. $P (P e r s o n i s f e m a l e A N D h a s a r i s k f a c t o r o f h o m o s e x u a l / b i s e x u a l) = 0$

e. $P (P e r s o n i s m a l e A N D h a s a r i s k f a c t o r o f I V d r u g u s e r) = \frac{463}{3059}$

f. $P (P e r s o n i s f e m a l e G I V E N p e r s o n g o t t h e d i s e a s e f r o m h e t e r o s e x u a l c o n t a c t) = \frac{136}{196}$

g. The Venn diagram shown below:

Step by step solution

Content Introduction

The completed data in table is as follow:

Explanation (Part a)

Suppose a person with AIDS in Santa Clara County is randomly selected, therefore the probability of P(Person is female) is given below:

$P (p e r s o n i s f e m a l e s) = \frac{t o t a l f e m a l e s}{T o t a l i n d i v i d u a l s} P (p e r s o n i s f e m a l e s) = \frac{255}{3059}$

Explanation (Part b)

Suppose a person with AIDS in Santa Clara County is randomly selected, therefore the probability of P(Person has a risk factor heterosexual contact).

$P (P e r s o n h a s a r i s k f a c t o r h e t e r o s e x u a l c o n t a c t) = \frac{T o t a l p e r s o n w h o h a s a r i s k f a c t o r h e t e r o s e x u a l c o n t a c t}{t o t a l i n d i v i u d u a l s} P (P e r s o n h a s a r i s k f a c t o r h e t e r o s e x u a l c o n t a c t) = \frac{196}{3059}$

Explanation (Part c)

Suppose a person with AIDS in Santa Clara County is randomly selected, therefore the probability of P(Person is female OR has a risk factor of IV drug user).

$P (P e r s o n i s f e m a l e O R h a s a r i s k f a c t o r o f I V d r u g u s e r) = \frac{255}{3059} + \frac{533}{3059} P (P e r s o n i s f e m a l e O R h a s a r i s k f a c t o r o f I V d r u g u s e r) = \frac{788}{3059}$

Explanation (Part d)

Suppose a person with AIDS in Santa Clara County is randomly selected, therefore the probability of P(Person is female AND has a risk factor of homosexual/bisexual).

$P (P e r s o n i s f e m a l e A N D h a s a r i s k f a c t o r o f h o m o s e x u a l / b i s e x u a l) . = 0$

explanation (Part e)

Suppose a person with AIDS in Santa Clara County is randomly selected, therefore the probability of P(Person is male AND has a risk factor of IV drug user)

$P (P e r s o n i s m a l e A N D h a s a r i s k f a c t o r o f I V d r u g u s e r) = \frac{463}{3059}$

Explanation (Part f)

Suppose a person with AIDS in Santa Clara County is randomly selected, therefore the probability of P(Person is female GIVEN person got the disease from heterosexual contact)

$P (P e r s o n i s f e m a l e G I V E N p e r s o n g o t t h e d i s e a s e f r o m h e t e r o s e x u a l c o n t a c t) = \frac{136}{196}$

Explanation (Part g)

A Venn diagram of one group females and the other group heterosexual contact is shown bellow:

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

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Short Answer

Step by step solution

Content Introduction

Explanation (Part a)

Explanation (Part b)

Explanation (Part c)

Explanation (Part d)

explanation (Part e)

Explanation (Part f)

Explanation (Part g)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Statistics

Pure Maths

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.