Dependent and Independent Events in Probability

The video tutorial explains probability using a marble example. It covers two cases: one where marbles are replaced after being drawn, leading to independent events, and another where they are not replaced, resulting in dependent events. The tutorial highlights how the sample space changes in each scenario, affecting the probability calculations.

What is the total number of marbles in the box?

• 3

• 6

• 9

• 12

In the first case, what happens after you pick the first marble?

• You give it to someone

• You discard it

• You replace it back in the box

• You keep it out of the box

What is the probability of picking a red marble first in the first case?

• 3/6

• 1/3

• 2/3

• 1/2

Why are the events in the first case considered independent?

• Because the marbles are not replaced

• Because the marbles are different colors

• Because the total number of marbles changes

• Because the marble is replaced, keeping the sample space the same

What is the probability of picking a blue marble first in the first case?

• 1/2

• 3/6

• 1/3

• 2/3

What is the probability of picking a blue marble second in the first case?

• 1/2

• 3/6

• 2/3

• 1/3

In the second case, what is different about the process?

• You replace the marble after picking

• You do not replace the marble after picking

• You pick three marbles instead of two

• You only pick blue marbles

What is the probability of picking a red marble first in the second case?

• 3/6

• 2/5

• 1/2

• 3/5

Why are the events in the second case considered dependent?

• Because the marbles are replaced

• Because the marble is not replaced, changing the sample space

• Because the total number of marbles remains the same

• Because the marbles are different colors

What happens to the probability of picking a red marble second in the second case?

• It remains the same

• It decreases

• It increases

• It becomes zero