11.2 Representing Outcomes
Design a tree diagram for problems 1-3.
1. Jessica has three skirts and four sweaters. How many possible outfits can she arrange given her clothing?
2. Kim loves ice cream. She has the option of vanilla, chocolate, or strawberry ice cream and she has different toppings to put on her ice cream cone. If she has sprinkles, hot fudge, and nuts to choose from, how many different ice cream cones can she create with those toppings?
3. There are five possible surfboard designs and two possible colors. How many possible surfboards can be created from these options?
4. A bag contains a red ball and blue ball. Nadir reaches in the bag and picks a ball out at random from the bag. He places it back into the bag. Nadir then reaches in the bag and picks another ball at random.
a. Draw a tree diagram to represent the possible outcomes in this problem.
b. What is the probability that Nadir picks a red ball on his second draw?
5. A teacher has a prize box on her front desk for when students do exceptional work in math class. Inside the box there are blue pencils, red pencils, and yellow pencils. The pencils are topped with either a sports or star eraser. Adriana completed a challenge problem for Ms. Cameron, and Ms. Cameron rewarded Adriana’s innovative problem-solving approach with a trip to the prize box. Adriana reaches into the box and picks out a prize.
a. Draw a tree diagram to represent the possible outcomes of this problem.
b. What is the probability that Adraina reaches into the box and picks out a red pencil with a star eraser?
6. Use the following Venn diagram to answer the question:
In the Venn diagram, list the outcomes for event A. List the outcomes for event B?
7. If the 2 ovals in the Venn diagram from problem 11 above represent events A and B, respectively, what is A and B?
8. Use the following Venn diagram to answer the question:
If the 2 ovals in the Venn diagram above represent events A and B, respectively, what is A or B?
9. In Jason's homeroom class, there are 11 students who have brown eyes, 5 students who are left-handed, and 3 students who have brown eyes and are left-handed. If there are a total of 26 students in Jason's homeroom class, how many of them neither have brown eyes nor are left-handed? Construct a Venn diagram to help you answer this question.