In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from $1$ to $10$, and one SuperBall is drawn (at random) from ten red balls numbered from $11$ to $20$. When you buy a ticket, you choose three numbers from $1$ to $10,$ and one number from $11$ to $20$. If the numbers on your ticket match the three white balls and the red SuperBall, then you win the jackpot. (You don't need to match the white balls in order). What is the probability that you win the jackpot?

BigBoiChungus Jul 22, 2021

#1**+2 **

Here is my take on this one:

Try again:

Re-take:

How many possible combos are there?

10 c 3 * 10 C1 = 1200 possible combos you have a 1 in 1200 chance of doing this

Matching two AND Superball

10 c 2 = 45

10 c 1 = 10 (for Superball) 45 * 10 = 450 you have a 450 out of 1200 chance of doing this

Matching two

45 out of 1200

matching three

120 out of 1200

matching superball

10 out of 1200

total prob of winning is then (1 + 450 + 45 + 120 + 10)/1200 = 626/1200 = 313/600

Hmmmmm.....getting closer perhaps!

ElectricPavlov Jul 22, 2021

#2**+2 **

We have two tasks.....choose the correct white balls and choose the correct SuperBall

Number of possible sets of C(10,3) = 120.....only one of these will win

So 1/120

And the probability of choosing the correct SuperBall = 1/10

So

(1/120) * (1/10) = 1 /1200

CPhill Jul 22, 2021

#3**+2 **

TRY number THREE:

1200 possibles 1 / 1200 chance to match that exactly

1 / 10 chance to match only superball 10 out of 1200

1 / 120 chance to match all 3 whites 10 out of 1200

3 ways to match 2 out of three whites 3 out of 1200 you could hit the superball too ( + 3/1200* 1/10 ?)

1 + 10 + 10 + 3 / 1200 = 24/1200 1/50 chance of a wining ticket so far....but I do not know how to compensate for the red note above

ElectricPavlov Jul 22, 2021