Question

In a​ state's Pick 3 lottery​ game, you pay ​$1.441.44 to select a sequence of three digits​ (from 0 to​ 9), such as 333333. If you select the same sequence of three digits that are​ drawn, you win and collect ​$363.23363.23. Complete parts​ (a) through​ (e). a. How many different selections are​ possible? 10001000 b. What is the probability of​ winning? 0.0010.001 ​(Type an integer or a​ decimal.) c. If you​ win, what is your net​ profit? ​$361.79361.79 ​(Type an integer or a​ decimal.) d. Find the expected value

Answer 1

Answer:

A) total number of possible selections = 10 x 10 x 10 = 1,000

B) the probability of winning = 1 / total number of possible selections = 1 / 1,000 or 0.001

C) in case you win, your net profit = $363.23 - $1.44 = $361.79

D) the expected value of your bet = (probability of winning x value of the winnings) - [(1 - probability of winning) x cost of the ticket] = (0.001 x $363.23) - [(1 - 0.001) x $1.44] = $0.36323 - (0.999 x $1.44) = $0.36323 - $1.43856 = -$1.07533 ≈ -$1.08