Thread: Data Management - Prob. Distributions

A lottery ticket has a $1,000,000 first price,a $25,000 second, and 5 $1000
third prizes. a total of 2,000,000 tickets are sold. If a ticket costs $2.00, what is the expected profit per ticket ?

I tried E(x) =Sum Xi . P(xi)

I am not getting 1.48 as an answer...

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2,000,000 tickets will sell for $ 4,000,000. Now the lottery company gives away one $ 1,000,000 award, one $ 25,000 award and five $ 1,000 awards.

Summing these awards up, you have $ 1,030,000 in awards given away.

So the lottery company expects to make a total of $ 4,000,000 - $ 1,030,000 = $ 2,970,000.

There are 2,000,000 tickets, so the expected profit per ticket is

Why did you add ?
Isnt the expectation E(X) = N x P ?

Doesn't really matter. Letting X = the amount a ticket buyer wins,



Now, if the ticket buyer payed $2 and can expect to win $0.515, this means the lottery company expects to make the rest from every ticket sold (i.e. $2 - $0.515 = $1.485)

This gives the same result as my first post.

Originally Posted by Faisal2007

Why did you add ?
Isnt the expectation E(X) = N x P ?

What's P meant to be? It looks to me like you're talking about the formula for the expected value of a random variable that follows a binomial distribution. The binomial distribution is not releveant here.

You need to review your class notes and/or textbook and get things straight.


I will add that the formula for the expected value of a binomial random variable is derived using the general definition of expected value:

.