Page 99 - Probability Demystified

88 CHAPTER 5 Odds and Expectation

2. There is one way to roll a sum of two and one way to roll a sum of 12;
there are 36 outcomes in the sample space.

Gain (X) $10 $5
2 34
Probability P(X)
36 36
2 34
EðXÞ¼ $10 þð $5Þ ¼ 4:17ðroundedÞ
36 36
Alternate Solution
2
EðXÞ¼ $15 $5 ¼ $4:17ðroundedÞ
36
3.

Gain, (X) $299 $1
1 499
Probability P(X)
500 500
1 499
EðXÞ¼ $299 þð $1Þ ¼ $0:40
500 500
Alternate Solution
1
EðXÞ¼ $300 $1 ¼ $0:40
500

1
4. PðHHÞ¼
4
1
EðXÞ¼ 0 ¼ $10 x
4
x ¼ $2:50
A person should pay $2.50 to play the game.
5.
Gain X $995 $495 $95 $5

1 2 5 992
Probability P(X)
1000 1000 1000 1000

1 2 5 992
EðXÞ¼ð$995Þ þ$495 þ$95 þð $5Þ ¼ $2:50
1000 1000 1000 1000