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 3,059documented 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(personisfemale)=2553059

b. P(personhasriskfactorhetrosexualcontact)=1963059

c. P(PersonisfemaleORhasariskfactorofIVdruguser)=7883059

d. P(PersonisfemaleANDhasariskfactorofhomosexual/bisexual)=0

e. P(PersonismaleANDhasariskfactorofIVdruguser)=4633059

f. P(PersonisfemaleGIVENpersongotthediseasefromheterosexualcontact)=136196

g. The Venn diagram shown below:

Step by step solution

01

Content Introduction

The completed data in table is as follow:

02

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(personisfemales)=totalfemalesTotalindividualsP(personisfemales)=2553059

03

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(Personhasariskfactorheterosexualcontact)=TotalpersonwhohasariskfactorheterosexualcontacttotalindiviudualsP(Personhasariskfactorheterosexualcontact)=1963059

04

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(PersonisfemaleORhasariskfactorofIVdruguser)=2553059+5333059P(PersonisfemaleORhasariskfactorofIVdruguser)=7883059

05

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(PersonisfemaleANDhasariskfactorofhomosexual/bisexual).=0

06

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(PersonismaleANDhasariskfactorofIVdruguser)=4633059

07

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(PersonisfemaleGIVENpersongotthediseasefromheterosexualcontact)=136196

08

Explanation (Part g)

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

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