Probability and Counting Principles

The video tutorial covers the basics of probability, starting with simple probability, which is defined as the number of desired outcomes divided by the total number of possible outcomes. Examples are provided to illustrate this concept. The tutorial then moves on to compound probability, which involves calculating the probability of multiple events occurring together. Finally, the video explains the concept of probability with and without replacement, using a marble example to demonstrate how the total number of outcomes changes depending on whether items are replaced after selection.

What is the basic formula for simple probability?

• Number of desired outcomes divided by total number of outcomes

• Total number of outcomes divided by number of desired outcomes

• Number of desired outcomes multiplied by total number of outcomes

• Total number of outcomes minus number of desired outcomes

In the first example, how many threes are there in the list?

• Two

• Four

• Three

• One

What is the total number of values in the list for the first example?

• 12

• 16

• 18

• 14

What is the probability of selecting a 3 from the list in the first example?

• 1/14

• 2/14

• 4/14

• 3/14

In the second example, which numbers are considered less than 3?

• 0 and 1

• 1 and 2

• 2 and 3

• 3 and 4

How many numbers less than 3 are there in the list for the second example?

• 6

• 7

• 8

• 9

What is the probability of selecting a number less than 3 from the list in the second example?

• 6/14

• 7/14

• 9/14

• 8/14

What is compound probability?

• Probability of an event happening twice

• Probability of multiple events happening together

• Probability of an event not happening

• Probability of a single event

How do you calculate compound probability?

• Divide the probabilities of each event

• Subtract the probabilities of each event

• Multiply the probabilities of each event

• Add the probabilities of each event

In the example of spinning a letter and tossing a coin, what is the probability of spinning an A?

• 1/3

• 3/4

• 1/2

• 1/4