Introduction to Contingency Tables: Videos & Practice Problems

A college tracks the number of male and female students who graduate with degrees in science and non-science fields:

What is the probability that a randomly selected science graduate is male?

A college tracks the number of male and female students who received bachelor's degrees in science and non-science fields in a given year:

What is the probability that a randomly selected bachelor's degree recipient earned a science degree, given that the student is male?

A statistics department reports the following data for students taking the final exam:

What is the probability that a student was a repeat test taker, given that the student failed the exam?

A university records the number of first-time and returning students who passed or failed a final exam. The data is as follows:

What is the probability that a student passed, given that the student was returning?

A hospital surveyed $1,000$ staff members — $500$ nurses and $500$ doctors — to find out whether they participate in wellness programs. The results are shown in the table below:

What is the probability that a randomly selected staff member participates in wellness programs, given that the staff member is a doctor?

A survey records the number of students enrolled in $3$ different types of courses and at $2$ different levels at a university. If a student is selected at random, what is the probability that the student is at the postgraduate level and enrolled in arts?

Fill in the blanks.

If $P(\text{rain}\mid \text{traffic})$ is written, it represents the probability of _______________ given _______________.

Given a contingency table with rows labeled 'Employed' and 'Unemployed' and columns 'Urban' and 'Rural', which cell corresponds to 'Unemployed & Rural'?

In a 2x3 contingency table of students by year (freshman, sophomore) and major (STEM, Arts, Business), what does a single interior cell entry represent?

In a contingency table of 200 survey respondents, 48 are 'female' and 'owns a bicycle'. What is the joint probability that a randomly chosen respondent is female and owns a bicycle?

A school survey records 120 students: 30 play football, 50 play basketball, 40 play neither. What is the marginal probability (as a decimal) that a randomly chosen student plays basketball?

A contingency table shows 80 employees: 20 are managers who work remote, 30 are managers who work on-site, and 30 are non-managers. If 50 employees are managers total, what is the probability an employee works remote given they are a manager?

In a 150-person study, the cell for 'smoker' and 'age 18-25' is 18. Express the joint probability as a simplified fraction, decimal, and percentage.

A contingency table shows 200 people: 80 are vaccinated (marginal P(vaccinated)=0.40). Among healthcare workers (50 people), 30 are vaccinated (P(vaccinated | healthcare)=0.60). Based on these probabilities, what can you conclude about the association between being a healthcare worker and vaccination status?

Which of the following wordings should you interpret as a conditional probability question?

Which entry in a contingency table gives the total number of observations in the entire dataset?

Which explanation correctly contrasts joint and conditional probability?

If a contingency table rows are 'Under 30' and '30 and over' and columns 'Owns pet' and 'Does not own pet', which cell would you read for people 'Under 30 & Owns pet'?

A contingency table records 250 survey participants. Column totals show 150 prefer online learning. What is the marginal probability that a randomly chosen participant prefers online learning (express as percentage)?

In a study of 500 households, 75 households both own a dog and subscribe to a home delivery service. What is the joint probability a randomly chosen household both owns a dog and subscribes to a delivery service? Provide the simplified fraction and decimal.