## anonymous one year ago 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.)

1. anonymous

|dw:1436664920532:dw|

2. anonymous

how is my set up wrong???

3. jim_thompson5910

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

4. anonymous

no idea :P

5. ybarrap

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

6. misty1212

HI!!

7. misty1212

you want a simple way to do it?

8. anonymous

yea I am adding it up but it is not right

9. misty1212

buy all 100 tickets at $10 each how much did you spend? 10. anonymous 1000? 11. misty1212 yes of course how much money do you get back? 12. misty1212 if that is not clear, i can explain, it is a very simple calculation 13. anonymous oh yea how would I calculate that? 14. misty1212 one$480 prize two $75 prizes 5$20 prizes

15. misty1212

$480+2\times 75+5\times 20=?$

16. anonymous

oh right right it is 730

17. misty1212

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

18. anonymous

270$19. misty1212 exactly averaged over the 100 tickets that is a loss of $$270\div 100=2.7$$ 20. jim_thompson5910 There are 4 tickets where you win$20, not 5 tickets

21. misty1212

ahh so there are !

22. anonymous

$-1.90?? 23. misty1212 that means you only get$710 back for a total loss of $290 24. 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 25. anonymous$-2.90

26. misty1212

right

27. anonymous

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

28. misty1212

let me look

29. anonymous

ok thnx

30. misty1212

ok i see why

31. 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

32. misty1212

same with all the other numbers

33. 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

34. misty1212

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

35. 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.