SOLUTION: A state lottery ticket costs $1. The probability of winning $1,000,000 is 0.0000001, the probability of winning $1,000 is 0.000005, and the probability of winning $10 is 0.0002.

Question 1026010: A state lottery ticket costs $1. The probability of winning $1,000,000 is 0.0000001, the probability of winning $1,000 is 0.000005, and the probability of winning $10 is 0.0002. Find the expected value (gain or loss) on one ticket.
I have created my chart with outcomes, probabilty & x* pr but am having trouble getting the expected vaule , can you please assist?
Found 3 solutions by Fombitz, Boreal, robertb:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Multiply the prize by the probability and then subtract the cost of the ticket.

Not a good deal at all.
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
x*p(x). Strictly speaking the probability of not winning is a little less for $10, because there are chances of winning one of the other two. Rounding error makes it small enough to ignore.
$1,000,000*1 X 10^(-7)=$0.10
$1000*0.000005=$0.60
$10*0.0002=$0.002.
Probability of losing is (1-.0000001-.000005-0.0002), but that is essentially 1. (it is 0.999749).
That is the loss.
The expected value is 0.702-0.999749=-0.2977, or -$-0.30 rounded to nearest cent.
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
To find the expected gain or loss, we proceed as follows:
If you win $1,000,000, your gain is $999,999. (Because of the $1 you spent in buying the ticket.) This has probability 0.0000001.
If you win $1,000, your gain is $999 (again because of similar reasoning as above). This event has probability 0.000005.
If you win $10, your gain is $9 (Should be easy now.) This event has probability 0.0002.
If you don't win at all, you gain -$1 (a loss!). This event has probability 1 - 0.0000001 - 0.000005 - 0.0002 = 0.9997949.
Thus the expected gain or loss is
999,999*0.000001 + 999*0.000005 + 9*0.0002 + (-1)*0.9997949 = -$0.893.
Therefore expect to lose when you buy a lottery ticket!

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