Back to Exercise: Construct and interpret two-way frequency tables

Exercises: Construct and Interpret Two-Way Frequency Tables

Work through each section in order. Read each two-way table carefully and
decide which total is the correct denominator BEFORE computing: the grand
total for marginal and joint probabilities, but a single row or column total
for a conditional probability. Write probabilities as fractions or decimals,
and remember that probabilities read from sample data are ESTIMATES, not
exact values.

Grade 10·21 problems·~35 min·Common Core Math - HS Statistics and Probability·group·hss-cp-a-4

Printable layout

Warm-Up: Reading a Two-Way Table

These problems review reading totals and relative frequencies from a table.

A survey classifies 120 students by grade and favorite subject.

	Math	Science	English	Total
10th grade	18	24	18	60
11th grade	22	16	22	60
Total	40	40	40	120

In this table, what does the number 24 represent?

The count of students who are in tenth grade AND favor science (a joint cell).

The total number of students who favor science.

The total number of tenth graders.

The probability that a student favors science.

Use the same table.

	Math	Science	English	Total
10th grade	18	24	18	60
11th grade	22	16	22	60
Total	40	40	40	120

A complete two-way table passes a structural check. Which statement is the correct check?

The row totals (60, 60) and the column totals (40, 40, 40) must each add up to the grand total, 120.

The four corner cells must add up to the grand total.

Every interior cell must equal the grand total divided by the number of cells.

The row totals and column totals must be equal to each other.

Use the same table.

	Math	Science	English	Total
10th grade	18	24	18	60
11th grade	22	16	22	60
Total	40	40	40	120

What fraction of ALL 120 students favor math? Give your answer as a fraction in lowest terms.

Fluency Practice

Compute each probability from the given table. Choose the correct denominator before you compute.

A pet survey records, for 50 people, whether they own a dog and whether they own a cat. Two cells are missing.

	Owns Cat	No Cat	Total
Owns Dog	12	13	?
No Dog	8	17	25
Total	20	?	50

What is the Owns Dog row total (the cell marked "?" in that row)?

Use the favorite-subject table.

	Math	Science	English	Total
10th grade	18	24	18	60
11th grade	22	16	22	60
Total	40	40	40	120

Find the JOINT probability $P(\text{eleventh grade and favors math})$ for a randomly selected student. Give your answer as a fraction in lowest terms.

Use the favorite-subject table.

	Math	Science	English	Total
10th grade	18	24	18	60
11th grade	22	16	22	60
Total	40	40	40	120

Find the MARGINAL probability $P(\text{favors English})$ for a randomly selected student. Give your answer as a fraction in lowest terms.

Use the favorite-subject table.

	Math	Science	English	Total
10th grade	18	24	18	60
11th grade	22	16	22	60
Total	40	40	40	120

Find the CONDITIONAL probability $P(\text{favors science} \mid \text{tenth grade})$ .

$\frac{24}{60} = 0.40$

$\frac{24}{120} = 0.20$

$\frac{24}{40} = 0.60$

$\frac{40}{120} \approx 0.33$

Use the favorite-subject table.

	Math	Science	English	Total
10th grade	18	24	18	60
11th grade	22	16	22	60
Total	40	40	40	120

Find the CONDITIONAL probability $P(\text{tenth grade} \mid \text{favors math})$ .

$\frac{18}{40} = 0.45$

$\frac{18}{60} = 0.30$

$\frac{40}{120} \approx 0.33$

$\frac{18}{120} = 0.15$

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