Conditional Probability: The Expected Utility

Conditional probability is like trying to find your keys in a dark house. You have to turn on the light, but first you need to figure out where the light switch is.

Let's break it down:

Example Time!

Suppose you have a box with 5 balls, and 3 of them are red. What is the probability of drawing a red ball, given that it's not the end of the world?

Here's a simple formula:

The Formula:

1. Define the probability of the event you're trying to predict (drawing a red ball): P(E) = 3/5 = 0.6

2. Define the probability of the event given the information (it's not the end of the world): P(I) = 1 (since it's not the end of the world)

3. Multiply the two probabilities together:

The Result:

P(E|I) = P(E) * P(I) = 0.6 * 1 = 0.6 (the probability of drawing a red ball, given it's not the end of the world)

Voilà! You've found your keys in the dark house.