Tree and Venn Diagrams · Example 10

(a) Which shows the probability that both kittens are tabby?
$\text{a}.\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)$ $\text{b}.\left(\frac{4}{9}\right)\left(\frac{4}{9}\right)$ $\text{c}.\left(\frac{4}{9}\right)\left(\frac{3}{8}\right)$ $\text{d}.\left(\frac{4}{9}\right)\left(\frac{5}{9}\right)$
(b) What is the probability that one kitten of each coloring is selected?
$\text{a}.\left(\frac{4}{9}\right)\left(\frac{5}{9}\right)$ $\text{b}.\left(\frac{4}{9}\right)\left(\frac{5}{8}\right)$ $\text{c}.\left(\frac{4}{9}\right)\left(\frac{5}{9}\right)+\left(\frac{5}{9}\right)\left(\frac{4}{9}\right)$ $\text{d}.\left(\frac{4}{9}\right)\left(\frac{5}{8}\right)+\left(\frac{5}{9}\right)\left(\frac{4}{8}\right)$
(c) What is the probability that a tabby is chosen as the second kitten when a black kitten was chosen as the first?
(d) What is the probability of choosing two kittens of the same color?

OpenStax, Statistics · §3.5 Tree and Venn Diagrams · Example 14