In a state\'s Pick 3 lottery game, you pay $1.23 to select a sequence of three d
ID: 3154900 • Letter: I
Question
In a state's Pick 3 lottery game, you pay $1.23 to select a sequence of three digits (from 0 to 9), such as 266. If you select the same sequence of three digits that are drawn, you win and collect $382.15 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 $ 1.23 in a certain state's Pick 4 game, the expected value is negative $ 0.85. Which bet is better, a $1.23bet in the Pick 3 game or a $ 1.23 bet in the Pick 4 game? Explain.
A.
The Pick 3 game is a better bet because it has a larger expected value.
B.
Neither bet is better because both games have the same expected value.
C.
The Pick 4 game is a better bet because it has a larger expected value.
Explanation / Answer
A) AS THE NUMBER TO BE CHOOSEN FROM = 0 TO 9 AND THE TOTAL NUMBER WE HAVE CAN BE WITH REPEATITION.
THEREFORE THE TOTAL NUMBER CAN BE FORMED = 10*10*10 = 1000
B) PROBABILITY OF WINNING
WE CAN WIN ONLY WHEN WE CHOOSE THE CORRECT NUMBER
THEREFORE PROBABILITY = 1/1000 = 0.001
C) IF I WIN THE NET PROFIT =
382.15 - 1.23 = 380.92
D) EXPECTED VALUE = E(X) = X1*P(X1)+X2*P(X2)+....+XN*P(XN)
382.15*1/1000 - 1.23*999/1000
= - 0.83