In a state\'s Pick 3 lottery game, you pay S$0.85 to select a sequence of three

Question

In a state's Pick 3 lottery game, you pay S$0.85 to select a sequence of three digits (from 0 to 9), such as 711. If you select the same sequence of three digits that are drawn. you win and collect $300.72. Complete parts (a) through (e). a. How many different selections are possible? b. What is the probability of winning? (Type an integer or a decimal.) c. If you win, what is your net profit? $ (Type an integer or a decimal) d. Find the expected value. $ (Round to the nearest hundredth as needed.) e. If you bet s0.85 in a certain state's Pick 4 game, the expected value is -$0.55. Which bet is better, a $0.85 bet in the Pick 3 game? Explain. A. Neither bet is better because both games have the same expected value. B. The Pick 3 game is a better bet because it has a larger expected value. C. The Pick 4 game is a better bet because it has a larger expected value.

Explanation / Answer

a) We have 10 digits and we have to select three digits .

Answer: 103 = 1000 possible selections

b) Probability of winning = 1/1000 = 0.001

c) Net Profit = Winning Amount - Paid Amount = 300.72-0.85 = $299.87

d) Expected Value

The expected value is the sum of all the possible outcomes weighted by their probability.

E[X] = XiPi

There are two outcomes: 1) you win and gain $299.87 and 2)You do not win and lose $0.85

The probability of outcome 1 is 0.001. The probability of outcome 2 is (1- 0.001) = 0.999.

Therefore,

E(X) = 0.001*299.87+0.999*(-0.85) = 0.29987-0.84915 =-0.55

Answer $ -0.55

e) Answer: Neither bet is better because both games have the same expected value.

Option A)

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