Question

in a states pick 3 lottery game, you pay $1.21 to select a sequence of three digits (from 0 to 9), such as 600. if you select the same sequence of three digits that are drawn, you win and collect $361.16. complete parts (a) through (d)
a. how many different selections are possible?
1000
b. what is the probability of winning?
0.001 (type an integer or a decimal.)
c. if you win, what is your net profit?
$ 359.95 (type an integer or a decimal.)
d. find the expected value.
$ (round to the nearest hundredth as needed.)

Explanation:

Step1: Calculate total selections

Each digit has 10 options (0-9), so total sequences = $10 \times 10 \times 10 = 1000$

Step2: Find winning probability

1 winning sequence out of 1000, so probability = $\frac{1}{1000} = 0.001$

Step3: Compute net profit if win

Net profit = Winnings - Cost = $361.16 - 1.21 = 359.95$

Step4: Calculate expected value

Expected value = (Win profit × Win probability) + (Loss × Loss probability)
$= (359.95 \times 0.001) + (-1.21 \times 0.999)$
$= 0.35995 - 1.20879 = -0.84884 \approx -0.85$

Answer:

a. 1000
b. 0.001
c. $359.95
d. $-0.85