Contingency Tables · Exercise 23

In a previous year, the weights of the members of a California football team and a Texas football team were published in a newspaper. The factual data were compiled into the following table. The weights in the column headings are in pounds.
\begin{array}{|c|c|c|c|c|}\hline \text{Shirt #} & \text{≤ 210} & \text{211–250} & \text{251–290} & \text{> 290} \\ \hline \text{1–33} & \text{21} & \text{5} & \text{0} & \text{0} \\ \hline \text{34–66} & \text{6} & \text{18} & \text{7} & \text{4} \\ \hline \text{66–99} & \text{6} & \text{12} & \text{22} & \text{5} \\ \hline\end{array}

For the following, suppose that you randomly select one player from the California team or the Texas team.
(a) Find the probability that his shirt number is from 1 to 33.
(b) Find the probability that he weighs at most 210 pounds.
(c) Find the probability that his shirt number is from 1 to 33 AND he weighs at most 210 pounds.
(d) Find the probability that his shirt number is from 1 to 33 OR he weighs at most 210 pounds.
(e) Find the probability that his shirt number is from 1 to 33 GIVEN that he weighs at most 210 pounds.

OpenStax, Statistics · §3.4 Contingency Tables · Exercise 23