Question

in a states pick 3 lottery game you pay 1.29 to select sequence of 3 digits. (from 0 to 9) such as 733. if seleced the same sequence of three digits that are drawn you win $307.14.

how many different selection are possible?

what is probabily of winning?

if win what is net profit?

find expected value?

if you bet $1.29 in certain states pick 4 the expected value is -$0.98. which bet is better a 1.29 in pick 3 or in pick 4?

Answer 1

a) Numbers can range from 000 to 999. There are 1000 possible solutions.

b) The probability of winning = 1 / 1000 = 0.001

(c) Net profit = Amount receive - Amount paid

= 307.14 - 1.29

= $ 305.85

(d)

Expected value= you will make a loss of 1.29 in 999 cases and a profit of 305.85 in 1 case

= (-1.29)* (999/1000) + (305.85)* ( 1/1000)

= -0.98286

= - $0.98(approx)

(e)

Expected values in both the bet is same So neither bet is better