Question

A lottery consists of one $2000 winner, three $500 winners, and ten $100 winners. a total of 1000 tickets are sold for $10 each. find the expected winnings for a person purchasing one ticket.

Answer 1

Answer: -5.5

 

WOKINGS

Given that the lottery has the following number of winners:

One $2000 winner

Three $500 winners

Ten $100 winners

 

Also Given,

A total of 1000 tickets are sold

Each ticket costs $10

 

The expected winning for a person purchasing one ticket is the sum of the products of the gain/loss and their corresponding probability.

 

There is one $2000 winner

There are 1000 tickets

The probability of winning $2000

= 1/1000

= .001

There are three $500 winners

There are 1000 tickets

The probability of winning $500

= 3/1000

= .003

 

There are ten $100 winners

There are 1000 tickets

The probability of winning $100

= 10/1000

= .01

 

Since each ticket costs $10

Everyone who buys a ticket automatically loses $10.

Therefore, the probability of losing $10 is 1

 

Now to calculate the expected winning for a person purchasing one ticket

= 2000(.001) + 500(.003) + 100(.01) – 10(1)

= 2 + 1.5 + 1 – 10

= -5.5

 

The expected winning is -5.5. This implies that a person playing this lottery can expect to lose $5.50 for every one ticket that they purchase.