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1
Inductive Logic
PHIL 111
Fall 2009
Chapters 8 and 9, Expected Value and Maximizing Expected value
Expected Value of A: Exp(A) = ∑[Pr(C
i
/A)U(C
i
)]
Exp(A) = Pr(C
1
/A)][U(C
1
)] +
[Pr(C
2
/A)][U(C
2
) + …etc.
(i.e. the expected value of an act is the sum of the products – utilities x probabilities)
1. [Freeloading] Nirit’s aunt Barb offers you a lottery ticket and you are free to accept it or not.
The expected value
of not accepting the lottery ticket is 0.
There were 100 tickets sold and the prize for owning the one ticket drawn is
$90.
What is the expected value of accepting the ticket?
2.
[Scammed] Little Calgon offers to sell you a lottery ticket for the charity auction at liberal Baptist church for one
dollar.
Again, you have a choice to accept the ticket or not.
The expected value of not accepting the lottery ticket is
0.
There were 100 tickets sold and the prize for owning the one ticket drawn is $90.
a. What is the expected value of accepting the ticket?
b. Is it in your best interest to purchase the ticket in the long run? Explain.
c. What is a fair price?
d. What is the fair price for this game?
e. How can you justify that this is the fair price? [see 3.]
3. [Fair Price] Little Calgon offers to sell you another lottery ticket for the charity auction for ninety cents.
Again,
you have a choice to accept the ticket or not.
The expected value of not accepting the lottery ticket is 0.
There were
100 tickets sold and the prize for owning the one ticket drawn is $90.
What is the expected value of accepting the
ticket?
Why is this price fair?
Would you loose or gain money by purchasing all 100 tickets?
4. [Fair Price and three possibilities] Imagine a raffle of 100 tickets, each with a 1/100 probability of being drawn.
The first ticket drawn will give a prize of $90 and the second ticket drawn gives a price of $9.
All subsequent draws
result in no gain or loss.
a. What is the fair price for this game?
b. What is the expected value of B: buying one ticket in the raffle for $1?
5.
Nirit’s cult asked him to participate in illegal street vending and he has been selling illegal commodities for over
a year.
The cost of the merchandise that he sells is $100 and his sales on a typical day came to $300.
From time to
time, Nirit gets caught for illegal vending and the fine is $100.
Nirit works on the street on Tuesday through
Saturdays and has found that he is ticketed about twice a week.
a. What is the expected value of working? Exp(W)
b. Do we know what Nirit will make today?
c. Suppose Nirit’s cult promises to pay all of his tickets if he is ticketed.
However the cult decides to charge Nirit
$50 a day for using their signature cart.
What is the expected value of working?
6. A standard roulette wheel has 18 reds, 18 blacks, and 2 zeros.
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This note was uploaded on 06/07/2011 for the course PHIL 111 taught by Professor Everett during the Fall '08 term at South Carolina.
 Fall '08
 Everett

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