Question

For a multistate lottery, the following probability distribution represents the cash prizes of the lottery with their corresponding probabilities. Complete parts (a) through (c) below. X (cash prize, $) Grand prize 200,000 10,000 100 P(x) 0.00000000877 0.00000023 0.000001734 0.000147996 0.004260186 0.008970789 .01261213 0.97400692623 4 3 0 0 (a) If the grand prize is $13,000,000, find and interpret the expected cash prize. If a ticket costs $1, what is your expected profit from one ticket? The expected cash prize is $ (Round to the nearest cent as needed.) What is the correct interpretation of the expected cash prize? O O A. On average, you will win $0.30 per lottery ticket. B. You will win $0.30 on every lottery ticket. O c. On average, you will profit $0.30 per lottery ticket. The expected profit from one $1 ticket is $ 7. (b) To the nearest million, how much should the grand prize be so that you can expect a profit? Assume nobody else wins so that you do not have to share the grand prize.

Answer 1

@ Grand price – $13,000,000 Expected winnings- E(X) - Ex.p(x). 6 EOS) - 13,000,000 x .000000008 Try) + ....--(3x 0. 0126122) + 0x0.99 = 0.11401 +0.046 + 0.0134 + 0.0142996 + 0.02982 +0.035863 + 0.037834 0.296 . Elx) a $ 0.30 is the expected winnings Expected profils per treket - $0.3-$1=${o.t) you loce fo.1 per trebat. cost of taket Ans: Aus on average, you will WIN $0.30 per lottery ticket On aurage you and not profit Expected profit from one ticket in $- 0.78 6 To expect a profit your wenning (Expected win) should be more than one dollar ($) Let Xo be the Grand prize amount, :. E(x) >1 :. Ecx) = (xqx 0. 0000000877 ) + Ex-pox) $1 = Čxgx 0. 0000 000 8+1) + 0.18199 u 1-0.18199 = xg + 0.18199 0.0000 0000 877) 0.00000000 877 • X9 C 94,00 0000 in Grand prize should be $94 million ① - ② No, because your chance of winning isd the properties of lottery, not the parente Note : Your Expected winnings will increase erminad by not your chances a