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.
. On the other hand, 
. Then: