The retail and service industries are another aspect of modern society where probability’s relevance can be seen. By studying data on their own service and their clientele, businesses can make informed decisions about how best to move forward in changing economies. Below is a table of data collected over a weekend at a local ice cream shop, Frankie’s Frozen Favorites. The table compares a customer’s flavor choice to their cone choice.
C = Chocolate
B = Butter Pecan
F = Fudge Ripple
CC = Cotton Candy
S = Sugar Cone
W = Waffle Cone
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Two-Way Table to Frequency Table
Include totals
Convert to marginal relative frequencies.
Convert to conditional relative frequencies for Juniors and Seniors.
P(A|J), P(A'|J), P(A|S) and P(A'|S).
Convert to conditional relative frequencies for attendance.
P(J|A), P(S|A), P(J|A') and P(S|A').
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Question 1
1.
Complete the table to help you answer the questions.
Question 2
2.
Find the following probabilities. Write the fraction (1st) and then the percent. Rounded to the nearest tenth.
P(C) = _______ = _______%
Question 3
3.
Find the following probabilities. Write the fraction (1st) and then the percent. Rounded to the nearest tenth.
P(B) = _______ = _______%
Question 4
4.
Find the following probabilities. Write the fraction (1st) and then the percent. Rounded to the nearest tenth.
P(F) = _______ = _______%
Question 5
5.
Find the following probabilities. Write the fraction (1st) and then the percent. Rounded to the nearest tenth.
P(CC) = _______ = _______%
Question 6
6.
Find the following probabilities. Write the fraction (1st) and then the percent. Rounded to the nearest tenth.
P(S) = _______ = _______%
Question 7
7.
Find the following probabilities. Write the fraction (1st) and then the percent. Rounded to the nearest tenth.
P(W) = _______ = _______%
Question 8
8.
By looking at the table and your calculations, would you say that there is a relationship between flavor and cone choice? Why or why not?
Same question...
Could you predict the cone choice from the flavor of ice cream?
Question 9
9.
Find the following probabilities. Write the fraction (1st) and then the percent. Rounded to the nearest tenth.
P(𝐶𝐶 ∩ W) = _______ = _______%
Question 10
10.
Find the following probabilities. Write the fraction (1st) and then the percent. Rounded to the nearest tenth.
P(S ∩ B) = _______ = _______%
Question 11
11.
Find the following probabilities. Write the fraction (1st) and then the percent. Rounded to the nearest tenth.
P(S|C) = _______ = _______%
Question 12
12.
Find the following probabilities. Write the fraction (1st) and then the percent. Rounded to the nearest tenth.
P(S|B) = _______ = _______%
Question 13
13.
Find the following probabilities. Write the fraction (1st) and then the percent. Rounded to the nearest tenth.
P(S|F) = _______ = _______%
Question 14
14.
Find the following probabilities. Write the fraction (1st) and then the percent. Rounded to the nearest tenth.
P(S|CC) = _______ = _______%
Question 15
15.
Find the following probabilities. Write the fraction (1st) and then the percent. Rounded to the nearest tenth.
P(W|F) = _______ = _______%
Question 16
16.
There are 16 juniors and 24 seniors on a debate team. Of those, 7 juniors and 19 seniors qualify for a state debate competition. Organize this information in a two-way table. Then find and interpret the marginal frequencies.
Question 17
17.
Convert to show marginal relative frequencies.
Question 18
18.
Convert to conditional relative frequencies for Juniors and Seniors.
Question 19
19.
Convert to conditional relative frequencies for if they qualified for the state competition.