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Basic Concepts Expected Value
If an event occurrs, the product of the payoff and the probability of the event
occurring is called the expected value. The event that is most closely related to
an expected value is a lottery.
Expected value of a lottery ticket Total amount of prize money
Number of lottery tickets
The lottery can be considered as a fair event when the ticket price is equal to
the expected value of a lottery ticket.
Example There are 100 lottery tickets that have different numbers, 00, 01,
02, , 98, and 99, written on them. If the prize money is given as
shown below, find the value of one lottery ticket.
Method of giving out the prize money
Draw a number from 100 lottery tickets.
If two digits of the lottery ticket number match with the corresponding
two digits of the number drawn, you will receive ten thousand dollars.
If one digit of the lottery ticket number matches with the corresponding
digit of the number drawn, you will receive one thousand dollars.
Ex. When the number drawn is 70,
Lottery ticket number: 70 The prize money: ten thousand dollars
Lottery ticket number: 71 The prize money: one thousand dollars
Lottery ticket number: 10 The prize money: one thousand dollars
Lottery ticket number: 07 The prize money: none
Class Notes
There is only one out of 100 lottery tickets that matches with the number drawn.
Therefore, there is only one lottery winner, and the prize money is thousand
dollars.
Excluding the first prize, there are out of 10 lottery tickets that have the
matching digit in the ones place with the number drawn.
The prize money is 1 (thousand dollars) thousand dollars.
Excluding the first prize, there are out of 10 lottery tickets that have the matching
digit in the tens place with the number drawn.
The prize money is 1 (thousand dollars) (thousand dollars).
Therefore, the total amount of prize money is 10 9 9 thousand dollars.
Since there are 100 lottery tickets, the value of one lottery ticket is
100 dollars.
95Number of Outcomes
If an event occurrs, the product of the payoff and the probability of the event
occurring is called the expected value. The event that is most closely related to
an expected value is a lottery.
Expected value of a lottery ticket Total amount of prize money
Number of lottery tickets
The lottery can be considered as a fair event when the ticket price is equal to
the expected value of a lottery ticket.
Example There are 100 lottery tickets that have different numbers, 00, 01,
02, , 98, and 99, written on them. If the prize money is given as
shown below, find the value of one lottery ticket.
Method of giving out the prize money
Draw a number from 100 lottery tickets.
If two digits of the lottery ticket number match with the corresponding
two digits of the number drawn, you will receive ten thousand dollars.
If one digit of the lottery ticket number matches with the corresponding
digit of the number drawn, you will receive one thousand dollars.
Ex. When the number drawn is 70,
Lottery ticket number: 70 The prize money: ten thousand dollars
Lottery ticket number: 71 The prize money: one thousand dollars
Lottery ticket number: 10 The prize money: one thousand dollars
Lottery ticket number: 07 The prize money: none
Class Notes
There is only one out of 100 lottery tickets that matches with the number drawn.
Therefore, there is only one lottery winner, and the prize money is thousand
dollars.
Excluding the first prize, there are out of 10 lottery tickets that have the
matching digit in the ones place with the number drawn.
The prize money is 1 (thousand dollars) thousand dollars.
Excluding the first prize, there are out of 10 lottery tickets that have the matching
digit in the tens place with the number drawn.
The prize money is 1 (thousand dollars) (thousand dollars).
Therefore, the total amount of prize money is 10 9 9 thousand dollars.
Since there are 100 lottery tickets, the value of one lottery ticket is
100 dollars.
95Number of Outcomes
