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A.P. Statistics Expected Value Practice
Date_______________
1.
An insurance company insures a person’s antique coin collection worth $20,000 for an annual premium of $300.
If the company figures that the probability of the collection being stolen is 0.002 what will be the company’s
expected profit?
2.
If a person rolls doubles when she tosses two dice, she wins $5. For the game to be fair, how much should she
pay to play the game?
3.
A person pays $2 to play a certain game by rolling a single die once. If a 1 or a 2 comes up, the person wins
nothing. If, however, the player rolls a 3, 4, 5, or 6, he or she wins the difference between the number rolled
and $2. Find the expectation for the game. Is it a fair game?
4.
A lottery offers one prize of $1000, one prize of $500, and five $100 prizes. One thousand tickets are sold at $3
each. Find the expectation if a person buys one ticket.
5.
From number four above, find the expectation if a person buys two tickets (assuming there is replacement
between draws).
6. One thousand tickets are sold at $1 each for an HD television. The television is valued at $350, what is the
expected gain if you purchase one ticket?
7.
A financial adviser suggests that his client select one of two types of bonds in which to invest $5000. Bond X
pays a return of 4% and has a default rate of 2%. Bond Y has a 2.5% return and a default of 1%. Find the
expected rate return and decide which bond would be a better investment. When the bond defaults, the
investor loses all the investment.
8.
A special six-sided die is made in which 3 sides have 6 dots, 2 sides have 4 dots, and 1 side has 1 dot. If the die
is rolled, find the expected value of the number of spots that will occur.
9.
In the PA lottery the Cash 5 is a game in which you choose 5 numbers ranging from 1 to 55 with no repeats, and
order does not matter. You pay $1 a ticket, and the minimum winnings are $100,000. What is the expected
value of playing the game when you buy one ticket?