Explore: Two-Way Tables Solutions

Two-Way Tables Solutions

A two-way table organizes information using rows and columns .
The information in the table cells can be counts, percentages, probabilities, etc .

Note

The rows of a table are horizontal. The columns of a table are vertical. The cells of a table are individual boxes where a row and a column intersect.

Combining Venn diagrams, sets, and two-way tables:

A’

$A \cap B$

A and B intersect

$A ’ \cap B$

not A and B

B’

$A \cap B ’$

A and not B

$A ’ \cap B ’$

not A and not B

Note

There are many ways to utilize a two-way table. Read the problem carefully to determine the best way to represent the information.

Example 5

The math department has 75 students enrolled, with the highest enrollment in Algebra (22 students) and Computer Science (19 students). Five students selected both courses, and the remaining students selected another math option.

Create the Venn diagram.
Create a two-way table.

$A = 22 - 5 = 17 Algebra only C = 19 - 5 = 14 Computer Science only 75 - (17 + 5 + 14) = 39 Other enrollment$

B)		A	A’	Total
	C	5	14	19
	C’	17	39
	Total	22		75

The probability of students enrolled in Algebra or Computer Science

$P (A \cup C) = \frac{(17 + 5 + 14)}{75} = \frac{36}{75} = \frac{12}{25}$

The probability of students in Algebra and Computer Science, or neither

$P (A \cap C \cup E) = \frac{(5 + 39)}{75} = \frac{44}{75}$