The NC Lottery has a game that picks 3 numbers You can bet 1

The NC Lottery has a game that picks 3 numbers. You can bet $1 by selecting three digits, each between 0 and 9. If you select the same sequence as the numbers that are drawn in the same order, you win and collect $500. The selection process would allow for a number to repeat, such as 111, 222, 333 or 122, 133, etc.

How many different selections are possible? (No decimal needed)

What is the probability of winning (Three decimals needed)

If you win, what is your net profit? (No decimal is needed)

Find the expected value (Two decimals are needed)

Solution

a)

There are 10 digits to choose from. Thus, there are 10^3 = 1000 selections possible. [ANSWER, 1000]

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b)

Thus, P(win) = 1/1000 or 0.001. [ANSWER]

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c)

The net profit is the prize minus the capital,

Profit = $500 - $1 = $499. [ANSWER]

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d)

E(x) = Sum (xP(x))

If you lose, you have a \"profit\" of -$1. Thus,

E(x) = 0.001*499 + (1-0.001)*(-1) = $ -0.50 [ANSWER]