Exploring Probability and Counting Techniques

A bag contains 3 red balls and 2 blue balls. A ball is drawn, not replaced, and then another ball is drawn. Create a tree diagram to represent all possible outcomes of drawing two balls.

• 3 branches for the first draw, 2 branches for the second draw

• 2 branches for the first draw, 3 branches for the second draw

• 5 branches for the first draw, 4 branches for the second draw

• 2 branches for the first draw, 2 branches for the second draw

How many different 3-letter combinations can be made from the letters A, B, C, and D if each letter can be used only once?

• 12

• 24

• 36

• 48

In a Venn diagram, set A has 10 elements, set B has 15 elements, and the intersection of sets A and B has 5 elements. How many elements are in the union of sets A and B?

• 20

• 25

• 30

• 35

A two-way table shows the number of students who prefer different types of music. If 30 students prefer pop, 20 prefer rock, and 10 prefer both, how many students prefer either pop or rock?

• 40

• 50

• 60

• 70

Create a tree diagram for flipping a coin twice. How many possible outcomes are there?

• 2

• 3

• 4

• 5

Using the fundamental counting principle, how many different outfits can be made with 3 shirts and 4 pants?

• 7

• 10

• 12

• 15

In a Venn diagram, if the probability of A is 0.3, the probability of B is 0.4, and the probability of A and B is 0.1, what is the probability of A or B?

• 0.6

• 0.7

• 0.8

• 0.9

A two-way table shows the number of students who like apples and bananas. If 15 students like apples, 10 like bananas, and 5 like both, how many students like only apples?

• 5

• 10

• 15

• 20