Q: Which formula correctly calculates the conditional probability $$P(A \mid B) in a $$contingency table?

$$P(A \mid B) = \frac{\text{Count in both A and B}}{\text{Total in B}}$$

Question 1

A university cafeteria surveys students about their preferred meal (breakfast or lunch) and whether they pay with cash or card. The results are displayed in a contingency table. Which of the following best describes a marginal distribution?

Accepted Answer

The percentage of all students who pay with card.

Question 2

Given a contingency table of gender (male, female) and preferred drink (coffee, tea), how would you calculate $$P(	ext{coffee} \mid 	ext{female})$$?

Accepted Answer

Divide the number of females who prefer coffee by the total number of females.

Question 3

A survey of 200 people records their favorite sport (soccer, basketball) and whether they own a pet. If 60 people like soccer and own a pet, what is the joint probability that a randomly selected person both likes soccer and owns a pet?

Accepted Answer

$$\frac{60}{200}$$

Question 4

In a contingency table of political party (Liberal, Moderate, Conservative) and pet ownership (Yes, No), which of the following questions asks for a conditional distribution?

Accepted Answer

What percentage of Liberals own a pet?

Question 5

A table shows time of day (Day, Night) and payment method (Credit, Cash). If 33% of day customers pay with credit and 56% of night customers pay with credit, what can you conclude about the independence of time of day and payment method?

Accepted Answer

The variables are not independent because the conditional distributions differ.

Question 6

Which formula correctly calculates the conditional probability $$P(A \mid B) in a $$contingency table?

Accepted Answer

$$P(A \mid B) = \frac{	ext{Count in both A and B}}{	ext{Total in B}}$$

Question 7

A contingency table shows class year (Freshman, Sophomore, Junior, Senior) and major (Biology, Chemistry, Physics). How would you find the marginal distribution of major?

Accepted Answer

Calculate the percentage of students in each major out of the total number of students.

Question 8

Suppose a table shows gender (male, female) and whether a person has a driver's license. If the conditional probability $$P(	ext{license} \mid 	ext{male}) is 0.80 $$and $$P(	ext{license} \mid 	ext{female}) is 0.81$$, what does this suggest?

Accepted Answer

Gender and having a driver's license are likely independent.

Question 9

A hospital records whether patients are smokers (Yes, No) and whether they have high blood pressure (Yes, No). Which of the following is a joint probability?

Accepted Answer

The probability that a patient is a smoker and has high blood pressure.

Question 10

In a survey, 120 out of 300 respondents are students, and 90 of those students prefer online classes. What is the conditional probability that a respondent prefers online classes given they are a student?

Accepted Answer

$$\frac{90}{120}$$

Question 11

A table shows employment status (Employed, Unemployed) and education level (High School, College). Which denominator would you use to find the marginal distribution of education level?

Accepted Answer

The total number of respondents.

Question 12

A study finds that $$P(	ext{Vegetarian} \mid 	ext{Liberal}) = 0.25$$ and $$P(	ext{Vegetarian} \mid 	ext{Conservative}) = 0.24. $$What does this indicate about the relationship between political view and being vegetarian?

Accepted Answer

Political view and being vegetarian are likely independent.

Question 13

Which of the following best describes a scenario where you would use a conditional distribution?

Accepted Answer

You want to know the percentage of night customers who use credit cards.

Question 14

A table shows favorite ice cream flavor (Chocolate, Vanilla, Strawberry) and age group (Child, Teen, Adult). If you are asked, 'Of all adults, what percentage prefer vanilla?', which type of distribution are you being asked to find?

Accepted Answer

Conditional distribution

Question 15

In a contingency table, which of the following is the correct interpretation of the joint probability $$P(A \cap B)$$?

Accepted Answer

The probability of being in both category A and category B.

Question 16

A table shows whether people exercise regularly (Yes, No) and whether they eat breakfast daily (Yes, No). If the conditional distributions of exercise for breakfast eaters and non-eaters are very different, what does this suggest?

Accepted Answer

Exercise and breakfast habits are not independent.

Question 17

A survey of 500 people records their favorite season (Spring, Summer, Fall, Winter) and whether they own a car. If 150 people prefer Summer and own a car, what is the joint probability that a randomly selected person both prefers Summer and owns a car?

Accepted Answer

$$\frac{150}{500}$$

Question 18

Which of the following phrases signals you should use a marginal distribution?

Accepted Answer

"Of all individuals surveyed..."

Question 19

A table shows students' class year and whether they live on campus. If you want to know the percentage of seniors who live on campus, which denominator should you use?

Accepted Answer

The total number of seniors.

Contingency Tables and Categorical Data Analysis

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