In a States Pick 3 lottery game you pay $1.31 to select a sequence of three digi
ID: 3258355 • Letter: I
Question
In a States Pick 3 lottery game you pay $1.31 to select a sequence of three digits from 0 to 9 such as 255. If you select the same sequence of three digits that are drawn you win and collect $474.97 complete Parts a through e
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 a dollar in $0.31 and a certain States Pick 4 game the expected value is -84 cents which bet is better a $1.31 bet in the Pick 3 game or $1. 31 bet in The Pick 4 game
Explanation / Answer
a) number of different selections = 10^3 = 1000
b) the probability of winning = 1/1000 = 0.001
c) if you win what is your net profit = 474.97 - 1.31 = 473.66
d) the expected value = 0.999*(-1.31) + 0.001*(473.66) = -0.835
e) in pick 4 game E(X) = -0.84
since -0.835 > -0.84
a $1.31 bet in the Pick 3 game is better