Dependent and Independent Events in Probability

The video tutorial explains dependent events in probability, focusing on how the occurrence of one event affects the probability of another. It uses examples involving marbles and machine parts to illustrate calculations of probabilities without replacement, emphasizing the concept of intersection in probability theory.

What is a dependent event in probability?

• An event that occurs with a fixed probability

• An event that is independent of any other event

• An event that affects the probability of another event

• An event that does not affect the outcome of another event

Which mathematical operation is used to find the probability of dependent events?

• Subtraction

• Division

• Multiplication

• Addition

In the marble problem, what is the initial probability of picking a green marble?

• 2 out of 16

• 6 out of 16

• 5 out of 16

• 3 out of 16

How does the probability change when a marble is picked without replacement?

• The total number of marbles remains the same

• The probability of the first event changes

• The probability of the second event is unaffected

• The total number of marbles decreases

What is the reduced probability of picking a green and then a yellow marble?

• 1/16

• 1/2

• 1/8

• 1/4

In the machine parts problem, what is the initial probability of picking a bad part?

• 5 out of 100

• 10 out of 100

• 1 out of 100

• 20 out of 100

What happens to the probability of picking a second bad part if the first is not replaced?

• It increases

• It decreases

• It remains the same

• It becomes zero

What is the reduced probability of picking two bad parts in a row?

• 1 out of 50

• 1 out of 495

• 1 out of 100

• 1 out of 25

What is the total number of parts left after picking one bad part?

• 98

• 100

• 99

• 97

How many bad parts are left after one is picked and not replaced?

• 2

• 3

• 4

• 5