Data Management, Math
posted by Jenna .
10 of your friends (including you..so 10 altogether) are going to have a draw between all of you. Each person gives $10 (for a total of $100). There will be five, $20 draws. One per week for 5 weeks.
For the first draw, every person gets a ticket. One ticket is picked from 10 tickets.
For the second draw, everyone gets a new ticket. Now, everyone (including the past winner) has two tickets. One ticket is picked from 20 tickets.
For the third draw, everyone gets a new ticket. Now, everyone (including the past winner) has three tickets. One ticket is picked from 30 tickets.
And so on until the draws are finished.
a) One of your friends says that you have a 1 in 10 chance each week to win. Since there are 5 draws, you have a 50% chance of winning at least once. Is your friend correct?
b) What is the expected size of the prize you would win?
c) Is this a fair game? Explain.
in week 1 you have a 1 in 10 chance to win, or 10%. In week 2 you have a 2 in 20 chance to win or 10% .... In week 5 you have a 5 in 50 chance to win, or 10%.
a) The probability that you always lose is .9^5 = .59049 -- so the probability that you win at least once is 1-.59049 = 40.941% -- your friend is incorrect.
b) the expected prize is 5 chances at .1*$20 = 5*.1*$20 = $10.
c) its a fair game. take it from here.
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