**Conditional Probability**

1. What is the textbook’s definition of probability?

2. If there are 3 green marbles and 4 red marbles in a bag, and you were asked to draw one without looking, what is the probability of drawing one green marble?

3. If you don’t put that marble back, what is the probability of drawing another green marble?

4. What is the textbook’s definition of conditional probability?

5. Using the above “marbles in the bag” scenario, what is a conditional probability question that you can make from it?

In §4.4 we are introduced to the concept of conditional probability. The notation P(A | B) denotes the probability of event A occurring given that we know event B has occurred.

Now consider the Monty Hall Problem introduced in the following videos:

__https://m.youtube.com/watch?v=4Lb-6rxZxx0__

6. After watching these videos, we know that if we are given the option to switch doors that, probabilistically speaking, it is in our best interest to switch. Why is the probability of winning NOT 50/50 when the contestant is given the opportunity to switch?