Expected value #2

While working on the study guide for tomorrow’s quiz I came across question #2, which says:

Suppose I can buy a lottery ticket for $1 to get 1 chance in 10,000 to win $10,000 and 99 chances in 10,000 to win $100. What is the expected value of that ticket?

I was a bit confused as how to go about finding the expected value of the ticket. Could anyone help lead me in the right direction??

Considering the fact that we pay $1 for the ticket, there are three possible net outcomes:

• We net $9999 with probability 1/10000 .
• We net $99 with probability 99/10000
• We net -$1 with probability
  
  1-\frac{1}{10000}-\frac{99}{10000} = \frac{99}{100}.
  
  

Thus, the expected value is

I’m confused because the second equation ( 9999/10000+ 9999/10000-99/100) equals 1.0098 and not 0.99.

@ren98christy
It’s not

it’s

I added the explicit multiplication symbol; it was just a space before.

1- (1/10,000 * 10,000 + 99/10,000 * 100)= 0.99