16.1.33 For a multistate lottery, the following probability with their correspon

Question

16.1.33 For a multistate lottery, the following probability with their corresponding probabilities. Questions distribution represents the cash prizes of the lottery Grand prize 200,000 10,000 100 0.00000000517 0.00000028 0.000001541 0.000152865 0.003872306 0.007572851 0.01327911 0.97512104183 (a) If the grand prize is $15,000,000, 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 S (Round to the nearest cent as needed) Enter your answer in the answer box and then dick Check Answer Clear Ah Check Answer TO

Explanation / Answer

a)

Consider:

Hence,

Thus,  
  
E(x) = Expected value = mean =    0.261481376 = $ 0.26 [ANSWER]

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b)

Expected profit = 0.26 - 1 = $ -0.74 [ANSWER]

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c)

So, we need an additional 1 - 0.261481376 = 0.738518624 to the expected value to have profit.

So, we need an additional

0.738518624/0.00000000517 = 142 846 929.20 = 143 M

to the grand prize.

Hence, we need the grand prize to be 15M + 143 M = 158 MILLION DOLLARS [ANSWER]

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OPTION B: NO, because the chance of winning is determined by the properties of lottery, not the payout. [ANSWER]

x P(x) x P(x) 15000000 5.17E-09 0.07755 200000 0.00000028 0.056 10000 0.000001541 0.01541 100 0.000152865 0.015287 7 0.003872306 0.027106 4 0.007572851 0.030291 3 0.01327911 0.039837 0 0.975121042 0

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