Algebra 2 Trig H
HW# 4 - Mathematical Expectation
Name_________________________________
1. You pay $.26, and draw a card at random from a normal 52-card deck. The payoffs are as follows:
Ace: Get $1.56
Face card: Get $.65
Any other card: Get nothing 
a. What is your mathematical expectation for this game?
b. In the long run, would you expect to gain money or lose money playing this game? How much money?
2. An expert marksman at archery has the following probabilities of hitting various rings on the target.
Color
a.
Probability
Points
Gold
0.20
9
Red
0.36
7
Blue
0.23
5
Black
0.14
3
White
0.07
1
What is her mathematical expectation on any one shot?
b. In a National Round, she shoots 48 arrows. What would you expect her score to be?
3. You play a game in which a dollar bill is selected at random. You win the bill if all 8 digits in its serial
number are different. What is your mathematical expectation, if you pay $.05 each time to play the
game?
4. Izzie’s mom offers to pay her $90 if she makes all A’s or to pay her $10 for each A she makes. However,
she must decide in advance which offer to accept. Izzie is a good student, and estimates her
probabilities of making A’s to be: .9 in Algebra 2 Trig H, .7 in English, .8 in Chemistry, and .6 in Spanish
a. Calculate her mathematical expectation if she chooses $10 per A.
b. Calculate her probability of making all A’s.
c.
Calculate her mathematical expectation if she chooses $90 for making all A’s.
d. Which offer should Izzie choose?
5. You pay a dollar and roll a die 3 times. If the outcome is a one at least two of the three times, you will
get back $10.00. Otherwise you get back nothing. What is your mathematical expectation for this
game?
6. An egg salesman has 5 dozen eggs that he will sell for $1.00 per dozen. Before they can be sold, they
must pass an inspection. Three eggs are selected at random. If all three are good, the inspection is
passed. If exactly one egg, the 5 dozen are rejected, and the salesman losses his cost of $.60 per
dozen. If two or more are bad, he loses his $.60 per dozen, and must pay a fine of $100 for trying to
sell such inferior products. Suppose that exactly two eggs are bad. What is the salesman’s
mathematically expected profit?