Can't justify 'correct' answer

#1
I thought I understood sampling without replacement fairly well, but this problem has me stumped as the answer that I calculate doesn't appear to be one of the available choices. The information I have that indicates the 'correct' answer seems wholly inaccurate (ie, I think the correct answer is wrong.).

A carton holds 18 eggs. If only 3 eggs are fertile, what is the probability of randomly selecting 2 eggs that are fertile if the selected eggs are not replaced?

A) 3/28
B) 9/64
C) 1/4
D) 3/4

I was under the impression that the correct answer would be (3/18)*(2/17) = 1/51, but I have reason to believe the 'correct' answer is 1/4.

Either I'm missing something (Probability > 0.5) or the 'correct' answer is wrong. Is there a justification/formula that indicates the answer is 1/4?

Thanks for any help anyone can provide.

Regards,

John M.
 

rogojel

TS Contributor
#2
A carton holds 18 eggs. If only 3 eggs are fertile, what is the probability of randomly selecting 2 eggs that are fertile if the selected eggs are not replaced?

A) 3/28
B) 9/64
C) 1/4
D) 3/4

I was under the impression that the correct answer would be (3/18)*(2/17) = 1/51, but I have reason to believe the 'correct' answer is 1/4.

Either I'm missing something (Probability > 0.5) or the 'correct' answer is wrong. Is there a justification/formula that indicates the answer is 1/4?

Thanks for any help anyone can provide.

Regards,

John M.
Hi,
this is a straightforward application of the hypergeometric distribution :
http://en.wikipedia.org/wiki/Hypergeometric_distribution
with N=18, K=3, n=2 and k=2 and it will give the same result you got, so I would say the 1/4 is way off the mark (by a factor of 10).

regards
rogojel