Pre-Calculus Final: Probability and combinatorics

A two-way table shows the number of students who prefer different types of music. If 30 students prefer rock, 20 prefer pop, and 10 prefer jazz, what is the probability that a randomly selected student prefers pop music?

In a Venn diagram, the probability of event A is 0.4, the probability of event B is 0.5, and the probability of both events A and B is 0.2. What is the probability of either event A or event B occurring?

• 0.7

• 0.9

• 0.6

• 0.8

Using the general multiplication rule, if the probability of event A is 0.5 and the probability of event B given A is 0.4, what is the probability of both events A and B occurring?

• 0.2

• 0.1

• 0.3

• 0.4

What is the probability of drawing a red card or a king from a standard deck of 52 cards?

How many permutations can be made from the letters in the word "MATH"?

• 12

• 24

• 16

• 20

In how many ways can a committee of 3 be selected from a group of 10 people?

• 120

• 45

• 720

• 30

What is the probability of selecting a committee of 3 people from a group of 10, where the order does not matter?

• 3

• 2.5

• 3.5

• 4

If an experiment is conducted 100 times and an event occurs 25 times, what is the empirical probability of the event?

• 0.25

• 0.5

• 0.75

• 0.2