Page 98 - Probability Demystified

CHAPTER 5 Odds and Expectation 87

Now the expected value of the game is

X $3 $2 $1 $1
1 15 75 125
P(X)
216 216 216 216

1 15 75 125
EðXÞ¼ $3 þ $2 þ $1 $1
216 216 216 216
17
¼ or 0.078 or about 8 cents:
216
Hence, on average, the house wins 8 cents on every game played by one
player. If 5 people are playing, the house wins about 5 8 cents ¼ 40 cents
per game.

PRACTICE

1. A box contains five $1 bills, two $5 bills, and one $10 bill. If a person
selects one bill at random, find the expected value of the draw.
2. If a person rolls two dice and obtain a sum of 2 or 12, he wins $15.
Find the expectation of the game if the person pays $5 to play.
3. Five hundred tickets are sold at $1 each for a color television set
worth $300. Find the expected value if a person purchased one ticket.
4. If a person tosses two coins and gets two heads, the person wins $10.
How much should the person pay if the game is to be fair?
5. A lottery offers one $1000 prize, two $500 prizes and five $100 prizes.
Find the expected value of the drawing if 1000 tickets are sold for
$5.00 each and a person purchases one ticket.

ANSWERS

1.
Gain (X) $10 $5 $1
1 2 5
Probability P(X)
8 8 8

1 2 5 1
EðXÞ¼ $10 þ $5 þ $1 ¼ $3 or $3:125
8 8 8 8