You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one $480 prize, two $75 prizes, and four $20 prizes. Find your expected gain or loss. (Round your answer to two decimal places.)

- anonymous

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- anonymous

|dw:1436664920532:dw|

- anonymous

how is my set up wrong???

- jim_thompson5910

the table looks good. Is your book showing something else?

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## More answers

- anonymous

no idea :P

- ybarrap

Now just sum the final column to get your expected gain/loss.

- misty1212

HI!!

- misty1212

you want a simple way to do it?

- anonymous

yea I am adding it up but it is not right

- misty1212

buy all 100 tickets at $10 each
how much did you spend?

- anonymous

1000?

- misty1212

yes of course
how much money do you get back?

- misty1212

if that is not clear, i can explain, it is a very simple calculation

- anonymous

oh yea how would I calculate that?

- misty1212

one $480 prize
two $75 prizes
5 $20 prizes

- misty1212

\[480+2\times 75+5\times 20=?\]

- anonymous

oh right right it is 730

- misty1212

you spent $1000 you get back $730
how much money did you lose?

- anonymous

270$

- misty1212

exactly
averaged over the 100 tickets that is a loss of \(270\div 100=2.7\)

- jim_thompson5910

There are 4 tickets where you win $20, not 5 tickets

- misty1212

ahh so there are !

- anonymous

$-1.90??

- misty1212

that means you only get $710 back for a total loss of $290

- misty1212

averaged over the 100 tickets it is a loss of \(290\div 100=2.9\) so your expected value i s\(-\$2.9\) per ticket

- anonymous

$-2.90

- misty1212

right

- anonymous

thanks so much cool way to solve it
but do you possibly know the mistake on my chart

- misty1212

let me look

- anonymous

ok thnx

- misty1212

ok i see why

- misty1212

when you win your prize of say $480 you have already spent $10
they do not refund your price of purchase, therefore your actual winnings are not $480 but rather $470

- misty1212

same with all the other numbers

- misty1212

i.e. when you win $75 it is a net gain of $65 and when you win $20 it is a net gain of $10

- misty1212

do it using your method but with the new numbers and you will get it

- ybarrap

The probability that you spend 10 dollars on the ticket if you play is 1:
|dw:1436674572521:dw|
$$
E[{\bf{X}}]=-10+.01(480)+.02(75)+.04(20)=-2.90
$$
Where \({\bf X}\) is your expected gain/loss.

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