Alottery sells 1000 tickets at $1 apiece. there is one winner who receives $100, and 5 second place winners who receive $50 each. what is the expected value of a ticket?

The expected value of a ticket is  - $0.625

Explanation: The expected value is calculated as:

E = ∑pₙxₙ

where pₙ is the probability that the event xₙ occurs.

We have 3 events, first place, where x = $99 and p = 1/1000, second place, where x = $49 and the probability is 5/1000 and the ones that dont win nothing, where x= -$1 and the probability is 996/1000

where i used 99$ and 49$ for the prices because i am discounting the $1 for the ticket.

then the expected value is:

E = ($99 + 5*$49 - 996*$1)/1000 = - $0.625

wich means that in average you lose money in this game

we know that the limit of both -1/x and 1/x as x approaches either positive or negative infinity is zero, therefore the limit of sin(x)/x as x approaches either positive or negative infinity is zero.