A basket contains 4 red balls and 5 blue balls. One ball is drawn and laid aside, and a second ball is drawn. Draw a tree diagram to represent the possible outcomes and probabilities. Use the tree diagram to answer the following questions.

(A) What is the probability of drawing a red ball and then a blue ball?

(B) What is the probability of drawing 2 blue balls?

Total balls = 9 initially;

8 balls remain after the first draw.

Tree diagram:

(A) P(red then blue).

$$P(R, \text{then } B) = \frac{4}{9} \times \frac{5}{8} = \frac{20}{72} = \frac{5}{18}$$

(B) P(two blue balls).

$$P(B, \text{then } B) = \frac{5}{9} \times \frac{4}{8} = \frac{20}{72} = \frac{5}{18}$$

Caution
Students should reduce the total count for the second draw while drawing without replacement. Using the original total for both draws is a common error.