MATH 131
Lab 4
8/11
The goal of this lab is to understand and find simple probabilities and conditional
probabilities, and to use the Multiplication Rule and the Addition Rule.
(1 point)
1. List the name for your qualitative variable, V1
2. Return to Lab 2. List the name for one of the largest slice in your
pie chart. (If a tie, choose either one.)
This name will be the label for Column 1 in your chart.
3. Categorize all of the other slices of your graph with a logical label.
(This will be very easy if your graph has only two slices; you use the
name of the smaller slice. If there are more than two slices, use the
labels ‘others’ or a better group name.)
This name will be the label for Column 2 in your chart.
4. List the name for your quantitative variable, V2.
5. Return to Lab 3, Part 1. What is the median for your V2 ?
6. The label for Row 1 will be values at or below the median. For
example, if the median age of senators is 57, Row 1 will be labeled
‘younger senators’ or ‘senators 57 or younger’ (  57 )
What is your label for Row 1?
7. The label for Row 2 will be values above the median. For
example, if the median age of senators is 57, Row 2 will be labeled
‘older senators’ or ‘senators over 57’. (  57 )
What is your label for Row 2?
Use the information above to create a table similar to this one.
Qualitative Variable, Political Party
Quantitative
Variable, V2
Age
8.
Younger Senators
Older Senators
Total
Democrat
6
19
25
Others
8
7
15
Total
14
26
40
Return to data in Lab 1 and count up the observations for each of the four cells in the
table. Place the sums in each cell and be sure that your frequencies add to 40. Also
record the totals for each row and each column.
Qualitative Variable, ______________
Total
Quantitative
Variable, V2
_________________
1
MATH 131
Lab 4
(2 points)
8/11
Find simple probabilities.
9.
Compute the probability of being in Row 1. Use the language of your data. (For
14
example, P(Younger senators) =
 0.350 ).
40
10.
Compute the probability of being in Row 2. Use the language of your data. (For
26
 0.650 ).
example, P(Older senators) =
40
11.
Compute the probability of being in Column 1. Use the language of your data. (For
25
 0.625 ).
example, P(Democrat) =
40
12.
Compute the probability of being in Row 1 and Column 1 using the appropriate
frequency from your table. Use the language of your data. (For example, P(Democrat
6
 0.150 ).
and younger) =
40
(3 points)
13.
14.
Find conditional probabilities.
Find the probability of being in Row 1, given Column 1. Use the language of your data.
(a) Comparing the probability in # 13 to the probability in # 9, decide if Rows and
Columns are independent. (b) Clearly explain your reasoning, using a complete
sentence and one of these phrases: equally likely, more likely or less likely.
Example
13. P(Younger, given Democrat) =
Your Data
13.
6
 0.240
25
14.
14. P(Younger) = 0.350
Since P(Younger, given Democrat) is less than
P(Younger), Democrats are less likely to be
younger. These are dependent events.
2
MATH 131
Lab 4
15.
16.
8/11
Find the probability of being in Column 1, given Row 2. Use the language of your data.
(For example, P(Democrat, given Older).
Comparing the probability in #15 to the probability in #11, determine if Rows and
Columns are independent. Clearly explain your reasoning, using a complete sentence
and one of these phrases: equally likely, more likely or less likely.
Example
15. P(Democrat, given Older) =
Your Data
15.
19
 0.731
26
16.
16. P(Democrat) = 0.625
Since P(Democrat, given Older) is higher than
P(Democrat), Older Senators are more likely to
be Democrats. These are dependent events.
Multiplication Rule
(1 point)
17.
If you choose two subjects from your sample, use the Multiplication Rule to find the
probability that they are both from Column 1.
Example
Your Data
P(Both Democrats) =
17.
P(Democrat and Democrat) =
25 24

=0.385
40 39
Addition Rule
Use the Addition Rule to find the probability of being in Row 1 or Column 1.
Use the Addition Rule to find the probability of being in Row 1 or Row 2.
(3 points)
18.
19.
Example
18. P(Younger or Democrat ) =
14 25
6


 0.825
40 40 40
19. P(Younger or Older) =
20.
Your Data
18.
19.
14 26

1
40 40
Consider your last two answers and list two mutually exclusive events for your data.
Explain your reasoning.
3