Independent vs Dependent Events in Probability

This video tutorial explains the difference between independent and dependent events using a bag of marbles. It covers calculating probabilities for pulling marbles of different colors, both with and without replacement. The tutorial provides examples for white, black, and striped marbles, illustrating how the probability changes based on whether the first marble is replaced or not. Key concepts include understanding how independent events do not affect each other, while dependent events do.

What defines an event as independent in the context of pulling marbles from a bag?

• When the color of the marble affects the outcome

• When different bags of marbles are used for each event

• When the same number of marbles is present for both events

• When the outcome of the first event affects the second event

What is the probability of pulling a white marble twice in a row, with replacement?

• 2/15

• 4/25

• 4/10

• 1/25

What is the probability of pulling a black marble twice in a row, with replacement?

• 1/20

• 1/25

• 2/10

• 1/45

How does the probability change when you do not replace the first marble after pulling it?

• It doubles

• It decreases

• It increases

• It remains the same

What is the probability of pulling a black marble followed by a white marble, without replacement?

• 1/45

• 2/25

• 8/45

• 4/45

In the context of the marble example, what signifies a dependent event?

• Replacing the marble after each pull

• Changing the color of the marbles

• Not replacing the marble after the first pull

• Using a different bag of marbles for each event

What is the probability of pulling a black marble followed by another black marble, without replacement?

• 4/45

• 1/25

• 2/25

• 1/45

What is the probability of pulling a white marble followed by a striped marble, with replacement?

• 1/25

• 4/25

• 2/15

• 8/45

What is the probability of pulling a white then a striped marble, without replacement?

• 2/15

• 1/25

• 4/25

• 8/45

How does the denominator change in dependent events?

• It decreases by 1

• It remains the same

• It increases by 1

• It doubles