Contingency Tables · Try It 3

relates the weights and heights of a group of individuals participating in an observational study.

$$\begin{array}{ccccc}\text{Ages}& \text{Tall}& \text{Medium}& \text{Short}& \text{Totals}\\ \text{Under 18}& \text{18}& \text{28}& \text{14}& \\ \text{18–50}& \text{20}& \text{51}& \text{28}& \\ \text{51+}& \text{12}& \text{25}& \text{9}& \\ \text{Totals}& & & & \end{array}$$

(a) Find the total for each row and column.
(b) Find the probability that a randomly chosen individual from this group is tall.
(c) Find the probability that a randomly chosen individual from this group is Under 18 and tall.
(d) Find the probability that a randomly chosen individual from this group is tall given that the individual is Under 18.
(e) Find the probability that a randomly chosen individual from this group is Under 18 given that the individual is tall.
(f) Find the probability a randomly chosen individual from this group is tall and age 51+.
(g) Are the events under 18 and tall independent?

OpenStax, Statistics · §3.4 Contingency Tables · Try It 3