Total possible outcomes = 12
Total cracked eggs = 3
Total non-cracked eggs = 9
The probability of having a cracked egg on the first pick would be 3/12 or 1/4.
On the other hand, assuming that we got a cracked egg on the first pick, the total possible outcomes would now be down to 11 and the number of non-cracked eggs would still be 9. Therefore, the probability of having a non-cracked egg on the second pick is 9/11.
So, the probability of selecting the first is cracked AND the second is non cracked is 9/44.
[tex]\frac{1}{4}\times\frac{9}{11}=\frac{9}{44}[/tex]