In the SmallState Lottery, three white balls are drawn (at random) from ten balls numbered 1 through 10, and a blue SuperBall is drawn (at random) from ten balls numbered through . When you buy a ticket, you select three numbers from 1-10 and one number from 11-20. To win the jackpot, the numbers on your ticket must match the three white balls and the SuperBall. (You don't need to match the white balls in order).
(a) If you buy a ticket, what is your probability of winning the jackpot?
(b) If you buy a ticket, what is your probability of winning a prize?
(a) The probability is 1/C(20,3) = 1/1140.
(b) nCr(20, 2) = 190 ways of selecting 2 from 20
nCr(10, 1) = 10 ways of selecting 1 from 10
To find the over all probability of winning,
Calculate the Harmonic Mean (19) and divide by 2
1/ (1//190 + 1/10) =9.5
So the probability is 1/9.5 = 2/19.