Reader’s Digest ran a sweepstakes in which prizes were listed along with the chances of winning: $1,000,000 ( 1 chance in 90,000,000), $100,000 ( 1 chance in 110,000,000), $25,000 ( 1 chance in 110,000,000), $5,000 ( 1 chance in 36,667,000), and $2,500 ( 1 chance in 27,500,000).
a) Assuming that there is no cost of entering the sweepstakes, find the expected value of the amount won for one entry.
b.) Find the expected value if the cost of entering this sweepstakes is the cost of postage stamp. Is it worth entering this contest?
2006-09-28 06:05:58 · 4 answers · asked by rocky 3 in Science & Mathematics ➔ Mathematics
First of all: The odds seem really strange that the chances of winning the grand prize are better than the $100K or $25K.
That said:
EV ($1mil) = 1,000,000/90,000,000 = $0.01111
EV ($100K) = 100,000/110,000,000 = $0.00091
EV ($25K) = 25,000/110,000,000 = $0.00023
EV ($5K) = 5,000/36,667,000 = $0.00014
EV ($2500) = 2,500/27,500,000 = $0.00009
Overall EV = $0.0125
Not worth the cost of a postage stamp (perhaps USPS is sponsoring it?) but it would be worth the cost of an email!
2006-09-28 06:19:56 · answer #1 · answered by Will 4 · 0⤊ 0⤋
Expected value is $0.012, which is a small fraction of the cost of a first class stamp, so it is not a good gamble.
2006-09-28 06:18:35 · answer #2 · answered by Sara Z 1 · 0⤊ 0⤋
It is your responsibility to do your own homework. Good luck!
2006-09-28 06:11:17 · answer #3 · answered by Kurt 2 · 0⤊ 3⤋
you are probably better off playing the local bingo. your chances are better
2006-09-28 06:15:04 · answer #4 · answered by LISA H 2 · 0⤊ 0⤋