Exploring Independent and Dependent Probability Concepts

The video tutorial covers the basics of probability, focusing on independent and dependent events. It explains how to calculate probabilities using examples with marbles, emphasizing the difference between independent events, where items are replaced, and dependent events, where items are not replaced. The tutorial includes step-by-step calculations and simplifications of fractions to illustrate these concepts.

What is the formula for calculating the probability of an event?

• Favorable outcomes / Total outcomes

• Total outcomes / Favorable outcomes

• Favorable outcomes + Total outcomes

• Total outcomes - Favorable outcomes

If you have 7 blue marbles and 3 red marbles, what's the probability of picking a red marble?

• 1/2

• 7/10

• 3/7

• 3/10

In independent probability, what must you do after picking a marble?

• Keep it aside

• Put it back

• Throw it away

• Give it to a friend

What is the probability of getting a blue marble after returning a red one back?

• 2/7

• 3/10

• 7/10

• 1/2

What changes in the setup when we switch to dependent probability?

• Marbles are not put back

• Number of marbles increases

• Color of marbles changes

• Size of marbles changes

What is the new probability of getting a blue marble after taking one and not putting it back?

• 3/9

• 7/9

• 6/9

• 7/10

After picking a red marble first in dependent probability, what's the probability of picking another red?

• 1/9

• 3/9

• 2/9

• 2/10

What's the probability of picking a blue marble first, then a red marble in dependent probability?

• 3/9

• 7/10

• 7/30

• 21/100

If you pick a blue marble and don't return it, what's the probability of picking another blue marble?

• 6/9

• 7/9

• 6/10

• 7/10

How does dependent probability differ from independent probability?

• Marbles change color after the first event

• More marbles are added after the first event

• Outcome of the second event depends on the first

• Outcome of the second event is independent of the first