Question

The two-way table below describes the members of the U.S Senate in a recent year. Male Female Democrats 47 13 Republicans 36 4 If we select a U.S. senator at random, what's the probability that the senator is a Democrat?

Two-way tables
ANSWERED
asked 2021-06-23
The two-way table below describes the members of the U.S Senate in a recent year.
Male Female
Democrats 47 13
Republicans 36 4
If we select a U.S. senator at random, what's the probability that the senator is a Democrat?

Answers (1)

2021-06-24
Let us determine the row/column total of each row/column, which is the sum of all counts in the row/column:
Male Female Total
Democrats 47 13 47+13=60
Respublicans 36 4 36+4=40
Total 47+36=83 13+4=17 60+40=100
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)=# of favorable outcomes/# of possible outcomes=\(\displaystyle\frac{{60}}{{100}}=\frac{{3}}{{5}}={0.6}={60}\%\)
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