Venn Diagrams · Exercise 31

In a previous year, the weights of the members of the San Francisco 49ers and the Dallas Cowboys were published in the San Jose Mercury News. The factual data were compiled into the following table.
\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 49ers or Cowboys.
(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, Introductory Business Statistics 2e · §3.5 Venn Diagrams · Exercise 31