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 adecimal.)
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.

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.

a=24; b=12

step-by-step explanation:

a/b=2: 1

a=2b

36/(1+2)=12

b=12

a=24