Counting and Probability


1. For dinner, Javier will choose one of three fish options and one of three side dishes. His choices for fish are salmon, trout, and halibut. His choices for side dishes are fries, cooked carrots, or coleslaw.

(a)
Draw a tree diagram for the sample space of all dinner combinations.

(b)
How many choices for dinner combinations does Javier have?
Answer:




2. The table shows the probabilities of winning or losing when the team is playing away or is playing at home.

(Check Image for Table)

(a)
Are the events “winning” and “playing at home” independent? Why or why not?
Show calculations to support your answer.


(b)
Are the events “losing” and “playing away” independent? Why or why not? Use probability rules and show calculations to support your answer.
Answer:


3. A box contains 4 black shirts, 8 blue shirts, 4 black pants, and 10 blue pants. Determine the probability of randomly selecting a blue piece of clothing or a pair of pants. Use P(A or B) = P(A) + P(B) - P(A and B) to explain your answer.
Answer: