## Introduction to Probability Models

Lecture 4

Qi Wang, Department of Statistics

Aug 27, 2018

## Reminders

- The first quiz will be on this
**Wednesday**
- The first homework is posted on the course website and due on
**Sep 7**

### Example 1

Drew is a risk taker. On any given weekend, Drew takes risks with or without monetary compensation.
He gets paid 20% of the time he takes risks. The risks involved are to either drink something weird
(like garlic butter) or do something silly (like shave his head into a mohawk).
Drew gets paid and drinks something weird 16% of the time. Drew does not get paid and drinks something weird 72% of the time.

- What is the probability Drew drinks something weird?
- What is the probability he does something silly?

### Example 2

You are previewing movies for your young nephew. You have 1284 movies available to view, 272 of which are G-rated. Your nephew
enjoys movies with puppets, which make up 94 of your G-rated movies. There are only 30 movies with puppets that are not G-rated. if
you happen to pick a movie that has puppets, what is the probability that it is G-rated?

## Multiplication Rule

- $P(A|B) = \frac{P(A\cap B)}{P(B)}$
- $P(A\cap B) = P(B) \times P(A|B) = P(A) \times P(B|A )$
- The probability that Events A and B both occur is equal to the
probability that Event B occurs times the probability that Event A occurs,
given that B has occurred

### Example 3

Three cards are dealt successively at random and without replacement from a standard
deck of 52 playing cards. What is the probability of receiving, in order, a king, a queen, and a jack?