Expected value

Question

In the Illinois pick 3 lottery game, you pay 50 cents to select a sequence of three digits.  If you select the same sequence of three digits that are drawn you win and collect $250.  There are 1,000 different selections possible, the probability of winning is .001 and the net profit is $249.50.  How do I find the expected value?

Answer 1

Q: In the Illinois pick 3 lottery game, you pay 50 cents to select a sequence of three digits. If you select the same sequence of three digits that are drawn you win and collect $250. There are 1,000 different selections possible, the probability of winning is .001 and the net profit is $249.50. How do I find the expected value?

 

A: The expected value is the sum of all the possible outcomes weighted by their probability.

 

E[X] = ∑X_iP_i 

 

There are two outcomes: 1) you win and gain $249.50 2)You do not win and lose 50 cents.

 

The probability of outcome 1 is 0.001. The probability of outcome 2 is 0.999.

 

Plugging these values into the formula yields:

 

E[X]=249.50*0.001-0.999*0.5=0.2495-0.4995=-25 cents

 

This means that on average you will lose 25 cents by playing.