6.1.31 Question Help For a multistate lottery, the following probability distrib

Question

6.1.31 Question Help For a multistate lottery, the following probability distribution represents the cash prizes of the lottery with their corresponding probabilities ca Grand prize 200,000 10,000 100 7 4 3 0.00000000759 0.00000023 0.000001696 0.000148543 0.004158808 0.008979319 0.01774577 0.96896562641 (a) If the grand prize is $18,000,000, 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 .33. Round to the nearest cent as needed.) What is the correct interpretation of the expected cash prize? A. On average, you will win $0.33 per lottery ticket. O B. On average, you will profit $0.33 per lottery ticket. C. You will win $0.33 on every lottery ticket. The expected profit from one $1 ticket is $ 0.67 (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 pize.

Explanation / Answer

Expecting a profit means the expected cash prize should be more than > 1

Let 'GP' be Grand prize.

Therefore

GP x 0.00000000759 + 0.196081 > 1 ; then a profit is expected ; as the cost of the ticket is '1'

therefore GP > (1 - 0.196081) / 0.00000000759) for a profit

GP > 105,918,242

Therefore Grand prize should be $106 million so that you can expect a profit.

X (Cash Prize) P(x) X.P(x) GP 0.00000000759 200000 0.00000023 0.046 10000 0.000001696 0.01696 100 0.000148543 0.014854 7 0.004158808 0.029112 4 0.008979319 0.035917 3 0.01774577 0.053237 0 0.96896562641 0 0.196081

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