+0  
 
0
99
10
avatar

https://web2.0calc.com/questions/please-help_23413

 May 29, 2020
 #1
avatar+732 
+1

hi guest!

 

so the problem is:

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 at least two of the white balls or match the red SuperBall, then you win a super prize. What is the probability that you win a super prize?

 

i see that it's an aops problem, so I'll only give you some hints.

 

there are \(\dbinom{10}{3}\cdot 10=1200\) total possibilities. 

 

since there are many cases to how you could win, its best to use complementary counting in this case. So, to have a losing ticket, you must have at most one correct white ball, and miss the superball.

 

1. Missing all 3 white balls: this happens if your ticket contains 3 of the 7 white numbers that weren't drawn, so there are \(\dbinom{7}{3}=35\) possibilities for that situation.

 

2. If you hit 1 white ball and miss the others: this happens if your ticket contains 1 of the 3 white numbers that were drawn and 2 of the 7 white numbers that weren't drawn, so there are \(3\dbinom{7}{2}=63\) possibilities for that case. 

 

from here, all you have to calculate are the cases with the superball and subtract them from the total since we are complementary counting.​

 

i think you can do the rest from there!

you got this!

ask me if you need any more help!

:)

 May 29, 2020
edited by lokiisnotdead  May 29, 2020
edited by lokiisnotdead  May 29, 2020
edited by lokiisnotdead  May 29, 2020
edited by lokiisnotdead  May 29, 2020
 #2
avatar
0

For the superball, I got:

 

There is only 10 numbers from 11 - 20. We take 1 out from those.

 

9 choose 1 = 9.

 May 29, 2020
edited by Guest  May 29, 2020
 #3
avatar+732 
0

ok so yea there are 9 cases with the superball. now just multiply 9 with the other 2 cases in my previous post.

lokiisnotdead  May 29, 2020
 #4
avatar+732 
0

and then subtract that from the total.

lokiisnotdead  May 29, 2020
 #5
avatar
0

I got 882/1200. Is that right?

 

63 + 35 = 98

 

98 * 9 = 882

Guest May 29, 2020
 #6
avatar+732 
0

ok now subtract that from the total since we are complementary counting (I'm assuming you know what that means)

lokiisnotdead  May 29, 2020
edited by lokiisnotdead  May 29, 2020
 #7
avatar
0

I got 318/1200. Is that right? If it is, THANK YOU SO MUCH FOR HELPING ME!

 May 29, 2020
 #8
avatar+732 
0

yep im pretty sure it is!

lokiisnotdead  May 29, 2020
edited by lokiisnotdead  May 29, 2020
 #9
avatar+732 
0

also remember to simplify!

lokiisnotdead  May 29, 2020
edited by lokiisnotdead  May 29, 2020
 #10
avatar+732 
0

just out of curiosity, was my answer right?

lokiisnotdead  May 29, 2020

14 Online Users

avatar
avatar