Question

# The two-way table below describes the members of the U.S Senate in a recent year.begin

Two-way tables

The two-way table below describes the members of the U.S Senate in a recent year.
$$\begin{array}{ccc} \hline &\text{Male}&\text{Female}\\ \text{Democrats}&47&13\\ \text{Republicans}&36&4\\ \hline \end{array}$$
If we select a U.S. senator at random, what's the probability that the senator is a Democrat?

2021-01-09

Let us determine the row/column total of each row/column, which is the sum of all counts in the row/column:
$$\begin{array}{c|cc|c} &\text{Male}&\text{Female}&\text{Total}\\ \hline \text{Democrats}&47&13&47+13=60\\ \text{Republicans}&36&4&36+4=40\\ \hline \text{Total}&47+36=83&13+4=17&60+40=100 \end{array}$$
The table contains 100 members in total (which is given in the bottom right corner of the table), while 60 of the 100 members are Democrats (since 60 is mentioned in the row ”Democrats” and in the column ”Total” of the given table).
The probability is the number of favorable outcomes divided by the number of possible outcomes:
$$P(Democrats)=\frac{\text{# of favorable outcomes}}{\text{# of possible outcomes}}=\frac{60}{100}=\frac{3}{5}=0.6=60\%$$
Result: $$\frac{3}{5}=0.6=60\%$$