Probability and Combinatorics Concepts

This video tutorial covers compound events, focusing on finding the number of outcomes using sample spaces and tree diagrams. It introduces the fundamental counting principle to simplify calculations and explores probability in compound events through examples like pizza options, rolling dice, and flipping coins. The lesson concludes with practice problems to reinforce learning.

What is the sample space in the context of compound events?

• A method to calculate probabilities

• A type of pizza crust

• A list of all possible outcomes for one or more events

• A mathematical formula

How many different pizza combinations are possible with thin and stuffed crusts and four styles?

• 16

• 4

• 12

• 8

What is a tree diagram used for in probability?

• To organize possible outcomes of compound events

• To solve algebraic equations

• To calculate the probability of a single event

• To list all possible outcomes of a single event

What does the fundamental counting principle allow you to do?

• Divide the number of outcomes for each event

• Multiply the number of outcomes for each event

• Subtract the number of outcomes for each event

• Add the number of outcomes for each event

How many possible outcomes are there when rolling a die and flipping a coin?

• 6

• 8

• 12

• 10

If you have 5 shirts, 4 pairs of pants, and 3 pairs of shoes, how many different outfits can you create?

• 40

• 60

• 30

• 50

What is the probability of rolling a number greater than 4 and flipping tails?

• 1/6

• 1/2

• 1/3

• 1/12

What is the probability of flipping two heads and one tail with three coin flips?

• 1/2

• 3/8

• 1/4

• 5/8

What is the probability of rolling double threes with two dice?

• 1/12

• 1/6

• 1/36

• 1/18

What is the probability of getting at least two tails when flipping three coins?

• 1/2

• 1/4

• 3/4

• 1