In a state\'s Pick 3 lottery game, you pay $1.33 to select a sequence of three d
ID: 3339859 • Letter: I
Question
In a state's Pick 3 lottery game, you pay $1.33 to select a sequence of three digits (from 0 to 9), such as 333. If you select the same sequence of three digits that are drawn, you win and collect $477.38. 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? s ] (Type an integer or a decimal.) d. Find the expected value. (Round to the nearest hundredth as needed.) e. If you bet $1.33 in a certain state's Pick 4 game, the expected value is $0.85. Which bet is better, a $1.33 bet in the Pick 3 game or a $1.33 bet in the Pick 4 game? Explain. A. Neither bet is better because both games have the same expected value. O B. The Pick 3 game is a better bet because it has a larger expected value OC. The Pick 4 game is a better bet because it has a larger expected value.Explanation / Answer
(a) How many different selections are possible?
Ans:Assuming each digit (0-9) is possible you have 10 x 10 x 10 = 1000 selections. That makes sense because the choices would be 000 to 999.
(b)What is the probability of winning?
Ans:You have 1 winning sequence out of 1000 total. The probability of winning is 1/1000= 0.001 = 0.1%
(c) If you win ,what is the your net profit?
Ans:If you win, your net profit is $476.88. That's because you win $477.38 but spent $0.50.
(d)Find the expected value
The expected value is:
1/1000 x $477.38 + 999/1000 x (-$0.50)
= 0.47738-0.4995
=-0.022
(e) If you bet $1.3 in a certain state's pick 4 game,the expected value is -$0.85 which bet is better ,a $1.33 bet in the pick 3 game or $1.33 bet in the pick 4 game?
Ans:Neither be tis better because both games have the same expected value