Question

# The two-way table summarizes data on the gender and eye color of students in a college statistics class.

Two-way tables

The two-way table summarizes data on the gender and eye color of students in a college statistics class. Imagine choosing a student from the class at random. Define event A: student is male and event B: student has blue eyes.
$$\begin{array}{c|cc|c} &\text{Male}&\text{Female}&\text{Total}\\ \hline \text{Blue}&&&10\\ \text{Brown}&&&40\\ \hline \text{Total}&20&30&50 \end{array}$$
Copy and complete the two-way table so that events A and B are mutually exclusive.

2020-11-10

Given
$$\begin{array}{c|cc|c} &\text{Male}&\text{Female}&\text{Total}\\ \hline \text{Blue}&&&10\\ \text{Brown}&&&40\\ \hline \text{Total}&20&30&50 \end{array}$$
A=Male B=Blue eyes
Two events are disjoint or mutually exclusive, if the events cannot occur at the same time.
In this case, events A and B are mutually exclusive, which then implies that there are no males with blue eyes and thus we need to enter 0 in the row Blue” and in the column ”Male” of the given table.
The remaining counts can then be determined using the row/column totals
$$\begin{array}{c|cc|c} &\text{Male}&\text{Female}&\text{Total}\\ \hline \text{Blue}&0&10-0=10&10\\ \text{Brown}&20-0=20&30-10=20&40\\ \hline \text{Total}&20&30&50 \end{array}$$
Result:
$$\begin{array}{c|cc|c} &\text{Male}&\text{Female}&\text{Total}\\ \hline \text{Blue}&0&10&10\\ \text{Brown}&20&20&40\\ \hline \text{Total}&20&30&50 \end{array}$$