Probability and Counting Principles

The video tutorial covers the concept of probability, focusing on compound events. It introduces the idea of sample space and demonstrates how to use tree diagrams to visualize possible outcomes. The fundamental counting principle is explained as a method to calculate the total number of outcomes. The tutorial also includes examples of calculating probabilities for compound events, such as rolling dice and flipping coins, and uses a game show scenario to illustrate the probability of winning at least one prize.

What is the sample space in probability?

• The number of times an event occurs

• The ratio of favorable outcomes to total outcomes

• The set of all possible outcomes of an event

• The likelihood of a single outcome

How many different sandwiches can be made with 2 types of bread and 4 types of meat?

• 6

• 8

• 10

• 12

What does the fundamental counting principle state?

• The probability of two independent events is the sum of their probabilities

• The sample space is the set of all possible outcomes

• The total number of outcomes is the product of the number of outcomes for each event

• The probability of an event is the ratio of favorable outcomes to total outcomes

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

• 6

• 8

• 10

• 12

What is the probability of rolling a number greater than 4 on a die?

• 1/3

• 1/6

• 1/2

• 2/3

If you roll a die, what is the probability of getting a number at most 4?

• 1/3

• 5/6

• 2/3

• 1/6

What is the probability of flipping tails on a coin?

• 1/3

• 1/4

• 1/2

• 2/3

How many different outfits can be made with 7 t-shirts, 4 pairs of jeans, and 3 pairs of shoes?

• 96

• 84

• 120

• 108

What is the probability of rolling a 5 or 6 on a die?

• 1/3

• 2/3

• 1/6

• 1/2

In a game show, what is the probability of winning at least one prize if you choose one box from each pair of three pairs?

• 1/8

• 3/8

• 7/8

• 5/8