SOLUTION: I was wondering if I could get confirmation if I got this problem right. 3 cans were accidentally filled with regular soda in a 12 pack of diet soda. 2 cans are selected randomly:

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Question 413624: I was wondering if I could get confirmation if I got this problem right.
3 cans were accidentally filled with regular soda in a 12 pack of diet soda. 2 cans are selected randomly:
a.) what is the probabilty that both cans are diet soda.
C(3,2)/(12,2)= 0.045
b.)what is the probabilty that both cans are regular.
C(10,2)/C(12,2)= 0.68
c.) what is the probabiltiy that exactly 1 can is diet and 1 is regular.
DIET: C(3,1)/C(12,1)= 0.12
REG: C(10,1)/C(12,1)= 0.12
Thanks for a ll your help,
Kim
Found 2 solutions by sudhanshu_kmr, Edwin McCravy:
Answer by sudhanshu_kmr(1152)   (Show Source): You can put this solution on YOUR website!

a) it is correct...

b) C(9,2)/C(12,2)

C)[C(3,1)*C(9,1)] / C(12,2)
= 27/66
=0.409


Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
I was wondering if I could get confirmation if I got this problem right.

You have the diet and the regular reversed, for your answer to (a) is 
the answer for (b).  

Your answer for (b) would be the answer for (a) except that you put 
10 where you should have 9.  There are 9 diet cans to choose from, 
not 10. 

Remember there are 9 diet cans and 3 regular cans, not the other way around.
The other tutor got them switched too.

You interpreted (c) as asking for two separate answers but it is just
one problem asking for 1 answer.
 
---------------------------------

3 cans were accidentally filled with regular soda in a 12 pack of diet soda. 2 cans are selected randomly:
a.) what is the probabilty that both cans are diet soda.

There are 9 diet cans
C(9,2)/C(12,2) = 0.5454... or 6/11

b.)what is the probabilty that both cans are regular.

There are 3 regular cans
C(3,2)/C(12,2)= 0.045... or 1/22

c.) what is the probability that exactly 1 can is diet and 1 is regular.

This is not two problems. It's just one problem and has just one answer.
[C(9,1)C(3,1)]/C(12,2) = (9*3)/66 = 9/22 

Edwin
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