Warm Up

1) Five different books are on a shelf. In how many different ways could you arrange them?

2) How many ways can gold, silver, and bronze medals be awarded for a race run by 8 people?

Solution #1The five books can be arranged in 5 · 4 · 3 · 2 · 1 = 5! = 120 ways.

Solution #2:Using the permuation formula we find P(8, 3) = 8!(8−3)! = 336 ways of them is r the second letter?

What is the expected value of winning it cost one dollar to win and if you win you get $35?

expected value is:−1×37⁄38 + 35×1⁄38 = −0.0526

Probability model to find expected value and standard deviation

mathematical representation of a random phenomenon. It is defined by its sample space and probabilities associated with each event

All probabilities add up to 1

A probability assigned for each possible outcome

A life insurance company charge $50 per year, they want to find out if they will have losses. They have 1000 policy holders who get:

$10,000 if die: 1 expected a year$5,000 if disabled: 2 expected a year$0: if nothing happens

How to find out about losses:

1. Set up probability model table

2. Find expected value

3. Find standard deviation

Outcome Probability

10000 1/1000 = .001

5000 2/1000 = .002

0 997/1000 = .997

Expected value 20

Standard Deviation for Probability Model

X = each outcomeP(x) = probability of each outcome

#1: find: outcome – expected value

#2: Square the answer for each outcome:

#3: multiply each answer by p(x):

#4: Add them all up:

#5: square root the sum