In a state\'s Pick 3 lottery game, you pay $1.27 to select a sequence of three d
ID: 3364313 • Letter: I
Question
In a state's Pick 3 lottery game, you pay $1.27 to select a sequence of three digits (from 0 to 9), such as 244. If you select the same sequence of three digits that are drawn, you win and collect $468.14.
a. How many different selections are possible?
b. What is the probability of winning?
c. If you win, what is your net profit?
d. Find the expected value.
e. If you bet $1.27 in a certain state's Pick 4 game, the expected value is negative $0.80. Which bet is better, a $1.27 bet in the Pick 3 game or a $ 1.27 bet in the Pick 4 game? Explain.
A. The Pick 4 game is a better bet because it has a larger expected value.
B. The Pick 3 game is a better bet because it has a larger expected value.
C. Neither bet is better because both games have the same expected value.
Explanation / Answer
a) Number of different selections possible = 10*10*10 = 1000
b) Probability of winning = 1/1000 = 0.001
c) Net profit = $468.14 - $1.27 = $ 466.87
d) Expected value = 0.001*466.87 - 0.999*1.27 = - 0.80
e) Neither bet is better because both games have the same expected value.
Option C is correct.