Unit 12 Part 2 Day 1 ­ Expected Value

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Welcome Back• Please grab your notebook and

your purple packet

BUT...

Unit 12 Part 2 Day 1 ­ Expected Value

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Today's Goal:I can define and use discrete random variable and geometric random variable.

I can calculate expected value given a table of probabilities or after constructing a tree diagram.

Random Variables, Expected Value, and

Counting Principle

Imagine that you are sitting near the rapids on the bank of a rushing river. Salmon are attempting to swim upstream. They must jump out of the water to pass the rapids. While sitting on the bank, you observe 100 salmon jumps and, of those, 35 are successful. Having no other information, you can estimate that the probability of success is 35% for each jump. 

What is the probability that a salmon will make it on its second attempt?

Unit 12 Part 2 Day 1 ­ Expected Value

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Random Variable: variable whose value depends on the outcome of a chance experiment.

Ex) the length of people's hair

Discrete Random Variable: a random variable that can take on only distinct values (integers).

Ex) the number of siblings for our class

Ex) the number of bottles of water purchased from a vending machine on any given day

Unit 12 Part 2 Day 1 ­ Expected Value

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Geometric Random Variable: a random variable that represents the number of trials needed to get the first success in a series of independent trials. Ex) the number free throw attempts needed before one goes in

Ex) the number attempts a girl scout makes before she sells a box of cookies

your dad gives you his set of keys and says open the cabin door.  

the length of a pencil in this room

how much money people have on them right now

how many songs a person has on their ipod

how many sibling a person has

the number of times a student takes the benchmark

Discrete Random Variable

Random Variable

Geometric Random Variable

Unit 12 Part 2 Day 1 ­ Expected Value

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A baseball player has a batting average of .300.

What is the probability that his first hit comes on his 6th at bat?

Thinking back to the salmon problem... 35% chance of success.

What is the probability that a specific salmon will not make it until its 4th attempt?

Expected Value:The average value you can expect for

your random variable.

E(x) =      xi p(xi)

Unit 12 Part 2 Day 1 ­ Expected Value

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box and depending on where it lands you win some money.  

You have a booth at the Minnesota State Fair where contestants play a game throwing the button into a 

The game:  They throw a button in.  It bounces around, inevitably.  They win the amount of money that it lands on.  

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20What can a contestant expect to win if they play the game?Find the "average" winnings:

.5($0)+.25($1) +.25($2) =$0.75

50% of the average comes from zero25% comes from 1 25% comes from 2

Unit 12 Part 2 Day 1 ­ Expected Value

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What is the lowest price you could charge and still make money?

$0.76

You could probably charge

$1.00 for them to play the game

so that you could make about $0.25

on each attempt

You enter a Charity Lottery• One Grand Prize of $20,000 • 20 additional prizes of $500 • Tickets only $10• ONLY 10,000 tickets will be sold 

EventProbability

$20,000 $500 $0

Unit 12 Part 2 Day 1 ­ Expected Value

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The world famous gambler from Philadelphia, Señor Rick, proposes the following game of chance. You roll a fair die. If you roll a 1, then he pays you $25. If you roll a 2, he pays you $5. If you roll a 3, you win nothing. If you roll a 4 or a 5, you must pay him $10, and if you roll a 6, you must pay him $15. Is Señor Rick loco for proposing such a game? Explain.

EventProbability

$25 $5 $0 $­10

Counting Principle:Say there are n1 ways to make a choice, n2 ways to make a 2nd choice, n3 ways to make a 3rd choice, etc...

Then the total # of possible outcomes is the product: n1 n2 n3 ....

ex)  Toss a coin 4 times.  How many possible outcomes are there?

Unit 12 Part 2 Day 1 ­ Expected Value

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ex) How many options for dinner does Kyle have if he has 2 entree choices, 3 veggie choices, and 2 dessert choices?

ex)  Toss a coin 4 times.  How many possible outcomes are there?

License Plates: How many are possible?3 letters followed by 4 numbers and any number and letter can repeat for NY?

1 number follwed by 3 letters then 2 numbers. 0 cannot start and you cannot repeat letters.

3 letters followed by 3 numbers and can't use I's, O's, or 0's

Unit 12 Part 2 Day 1 ­ Expected Value

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ex) There are 4 books on a shelf.  How many ways can you arrange them?

How are you doing? I can calculate expected value given a table of probabilities or after constructing a tree diagram.

1 - Complete Worksheet located G.C.

2 - Check Answers - if posted

3 - Complete Quiz #5 - if you finished

Unit 12 Part 2 Day 1 ­ Expected Value

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Unit 12 Part 2 Day 1 ­ Expected Value

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