An experiment consists of tossing a nickel, a dime and a quarter. Of interest is the side the coin lands on.
List the sample space.
Let
be the event that there are at least two tails. Find
.
Let
be the event that the first and second tosses land on heads. Are the events
and
mutually exclusive? Explain your answer in 1 - 3 complete sentences, including justification.
Yes
Consider the following scenario:
Let
Let
Let
Find
.
Are
and
mutually exclusive? Why or why not?
Are
and
independent events? Why or why not?
Find
.
Find
.
and
mutually exclusive events.
;
. Find
.
0
and
are independent events.
.Find
.
and
are mutually exclusive events.
;
. Find:
=
=
=
0
0
0.63
and
are independent events.
;
. Find
.
and
are independent events.
Rewrite the basic Addition Rule
using the information that Y and Z are independent events.
Use the rewritten rule to find
if
and
.
0.5
and
are mutually exclusive events.
;
Explain why the following statement MUST be false:
.
Find:
.
Are
and
independent or dependent events? Explain in a complete sentence.
The following are real data from Santa Clara County, CA. As of a certain time, there had been a total of 3059 documented cases of AIDS in the county. They were grouped into the following categories (
Source: Santa Clara County Public H.D. ):
Homosexual/Bisexual
IV Drug User*
Heterosexual Contact
Other
Totals
Female
0
70
136
49
____
Male
2146
463
60
135
____
Totals
____
____
____
____
____
* includes homosexual/bisexual IV drug users
Suppose one of the persons with AIDS in Santa Clara County is randomly selected. Compute the following:
=
=
=
=
=
=
Construct a Venn Diagram. Make one group females and the other group heterosexual contact.
The completed contingency table is as follows:
Homosexual/Bisexual
IV Drug User*
Heterosexual Contact
Other
Totals
Female
0
70
136
49
255
Male
2146
463
60
135
2804
Totals
2146
533
196
184
3059
* includes homosexual/bisexual IV drug users
0
Solve these questions using probability rules. Do NOT use the contingency table above. 3059 cases of AIDS had been reported in Santa Clara County, CA, through a certain date. Those cases will be our population. Of those cases, 6.4% obtained the disease through heterosexual contact and 7.4% are female. Out of the females with the disease, 53.3% got the disease from heterosexual contact.
Construct a Venn Diagram. Make one group females and the other group heterosexual contact. Fill in all values as probabilities.
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Source:
OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
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