Question

In a​ state's pick 3 lottery​ game, you pay ​$ to select a sequence of three digits​ (from 0 to​ 9), such as. If you select the same sequence of three digits that are​ drawn, you win and collect ​$. Complete parts​ (a) through​ (e).

Answer 1

The number of possible selections, probability of winning, net profit, expected value are respectively; A) 1000 B) 0.001 C) $382.8 D)  -$0.95

How to find expected value?

A) We are told that you want to select a sequence of three digits​ (from 0 to​ 9).  This means that there will be 10 numbers in total,

Since there are 3 lottery games, then;

Number of possible selections = 10³ = 1000

B) Probability of winning = one outcome/total outcomes

Thus;

P(winning) = 1/1000

P(winning) = 0.001

C) Net profit = winning amount - paid amount

Thus;

Net Profit = 384.13 - 1.33

Net Profit = $382.8

D) Formula for Expected value is;

E(x) = (net profit * winning probability) - (paid amount * lost probability)

Thus;

E(x) = (382.8 * 0.001) - (1.33 * 0.999)

E(x) = - $0.95

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