Sampling senators The two-way table below describes the members of the U.S Senate in a recent year. Male Female Democrats $4713$ Republicans $364$

(a) Who are the individuals? What variables are being measured?

(b) If we select a U.S. senator at random, what’s the probability that we choose

• a Democrat?
• a female?
• a female Democrat?
• a female or a Democrat?

A two-way table is presented that lists the members of the United States Senate from the previous year.

An event is a subset of an experiment's total number of outcomes. The ratio of the number of elements in an event to the number of total outcomes is the probability of that occurrence and the use of the complimentary rule.

To begin, it is necessary to comprehend the terms individual and variable:

Individuals: These are the objects that the data collection describes.

The study's variable is the topic under investigation. As a result, an individual is considered a "member of the United States Senate" for the purposes of a particular study. Political affiliation and gender are the variables.

The total number of possible outcomes is: $47+13+36+4=100$

As a result, the probability of being a Democrat is: probability =$\frac{47+13}{100}=0.60.$

Female probability: probability =$\frac{13+4}{100}=0.17$

Female democrats have a probability of =$\frac{13}{100}=0.13$

Probability of being a woman or a democrat: =$\frac{47+13+4}{100}=0.64$