Proving Independence Numerically

The video tutorial explains the concept of probability and how to determine if events are independent using the independence formula. It covers conditional probability and provides examples using a die roll, a coin flip, and a two-way table to illustrate the process of proving independence numerically.

What is the probability of rolling a 4 on a six-sided die?

• 1/2

• 1/12

• 1/3

• 1/6

How do you determine if two events are independent?

• If the probability of one event does not affect the other

• If both events are mutually exclusive

• If the probability of one event affects the other

• If both events have the same probability

In the die roll example, what is the probability of rolling an even number?

• 1/6

• 1/4

• 1/3

• 1/2

What is the probability of rolling a 4 given that an even number is rolled?

• 1/2

• 1/6

• 1/3

• 1/4

In the die roll and coin flip example, what is the probability of flipping heads?

• 1/6

• 1/3

• 1/2

• 1/4

What is the probability of rolling a 4 and flipping heads?

• 1/12

• 1/6

• 1/3

• 1/2

How can you prove independence using the probability of heads given 4?

• By showing it equals the probability of neither event

• By showing it equals the probability of both events

• By showing it equals the probability of flipping heads

• By showing it equals the probability of rolling a 4

In the two-way table example, what is the probability of buying candy?

• 1/2

• 1/3

• 1/4

• 1/5

What is the probability of buying both popcorn and candy?

• 1/4

• 1/2

• 1/5

• 3/20

Are buying popcorn and candy independent events?

• No, because they are dependent

• Yes, because the probabilities are equal

• No, because the probabilities are not equal

• Yes, because they are mutually exclusive