In a state\'s Pick 3 lottery game, you pay $1.38 to select a sequence of three d
ID: 3266668 • Letter: I
Question
In a state's Pick 3 lottery game, you pay $1.38 to select a sequence of three digits (from 0 to 9), such as 222. If you select the same sequence of three digits that are drawn, you win and collect $403.94.
Complete parts (a) through (e).
a. How many different selections are possible?
1000
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 $ 1.38 in a certain state's Pick 4 game, the expected value is $0.98.
Which bet is better, a $1.38 bet in the Pick 3 game or a $1.38 bet in the Pick 4 game? Explain.
A. Neither bet is better because both games have the same expected value.
B. The Pick 4 game is a better bet because it has a larger expected value.
Explanation / Answer
a. how many diffrent selections are possible: 10^3 = 1000
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b. what is the probability of winning:1/1000
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c. If you win, your net profit is $402.56.. That's because you win $403.94. but spent $1.38
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d. Pick 4 game expected value:
E(x) = (1/1000)(402.56)+(999/1000)(-1.38) = -0.97
A.Neither bet is better because both games have the same expected value.