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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?

 Jul 22, 2021
 #1
avatar+34315 
+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!

 Jul 22, 2021
 #2
avatar+121054 
+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

 

  cool cool cool

 Jul 22, 2021
 #3
avatar+34315 
+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

 Jul 22, 2021

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