Question

In a​ state's Pick 3 lottery​ game, you pay ​$1.15 to select a sequence of three digits​ (from 0 to​ 9), such as 966. If you select the same sequence of three digits that are​ drawn, you win and collect ​$258.35. Complete parts​ (a) through​ (e).
a. How many different selections are​ possible?
b. What is the probability of​ winning? ​(Type an integer or a​decimal.)
c. If you​ win, what is your net​ profit? ​​(Type an integer or a​ decimal.)
d. Find the expected value. ​$ (Round to the nearest hundredth as​ needed.)
e. If you bet $ 1.15 in a certain​ state's Pick 4​ game, the expected value is negative −$0.89. Which bet is​ better, a ​$1.15 bet in the Pick 3 game or a $ 1.15$ 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.
C. The Pick 3 game is a better bet because it has a larger expected value.

Answer 1

Answer:

A) 1000 different selections

B) probability of winning = 0.001

C) Net profit on winning = $257.20

D) E(y) = -0. 89165

E) Option B - The Pick 4 game is a better bet because it has a larger expected value.

Step-by-step explanation:

A) For the different selections possible, since each of the digits from 0 - 9 can take a total of 10 digits, then the different selections possible will be = 10³ = 1000 different selections

B) To find the probability of winning, since only one pick can be a winning one. Thus probability of winning = 1/1000 = 0.001

C) Net profit on winning = Amount won - Amount staked

Amount won = ​$258.35

Amount staked = ​$1.15

Thus;

Net profit on winning = ​$258.35 - ​$1.15

Net profit on winning = $257.20

D) If we call the net profit "y", then Expected value is:

E(y) = 257.2(0.001) - 1.15(1 - 0.001)

E(y) = 0.2572 - 1.14885

E(y) = -0. 89165

E) We are told that:If you bet $ 1.15 in a certain​ state's Pick 4​ game, the expected value is negative −$0.89

The expected value of -0.89 in pick 4 is better than that in pick 3 because it's larger.