1. In the SmallState Lottery, three white b***s are drawn (at random) from twenty b***s numbered 1 through 20, and a blue SuperBall is drawn (at random) from ten b***s numbered 21 through 30. When you buy a ticket, you select three numbers from 1-20 and one number from 21-30. To win the jackpot, the numbers on your ticket must match the three white b***s and the SuperBall. (You don't need to match the white b***s in order). If you buy a ticket, what is your probability of winning the jackpot?

2. In the SmallState Lottery, three white b***s are drawn (at random) from twenty b***s numbered 1 through 20, and a blue SuperBall is drawn (at random) from ten b***s numbered 21 through 30. When you buy a ticket, you select three numbers from 1-20 and one number from 21-30. To win a prize, the numbers on your ticket must match at least two of the white b***s or must match the SuperBall. If you buy a ticket, what is your probability of winning a prize?

Thanks for helping me!

Mellie Apr 9, 2015

#1**+37 **

Best Answer

1. For the first one, we have this many possibile outcomes :

C(20,3) * 10 = 11,400 ...so....the probability of winning on one ticket is 1 /11,400 = 0.0000877192982456 = about .0088%

CPhill Apr 10, 2015

#3**+15 **

2. For the second one.....

Let A be the probabilty of choosing 3 b***s out of 20

Let B be the probability of choosing one ball out of 10

So

P(P or B) = 1/C(20,3) + 1/10 = 1/1140 + 1/10 = 23/228 = about 10%

CPhill Apr 10, 2015

#4**+12 **

I get a slightly different answer for the second part:

prob of matching 3 white b***s = 3/20 * 2/19 * 1/18 = 6/(20*19*18)

prob of matching 1st and 2nd but not 3rd = 3/20 * 2/19 * 17/18 = 6*17/(20*19*18)

prob of matching 1st and 3rd but not 2nd = 3/20 * 17/19 * 2/18 = 6*17/(20*19*18)

prob of matching 2nd and 3rd but not 1st = 17/20 * 3/19 * 2/18 = 6*17/(20*19*18)

prob of matching blue ball = 1/10

Overall probability = 6*(1+3*17)/(20*19*18) +1/10 = 83/570 ≈ 0.146

I think Chris's probability (23/228) is that of getting *all three* white b***s or the blue ball, rather than *at least two* white b***s or the blue ball.

.

Alan Apr 10, 2015