I'm working on my last weak area before I am going to take the GMAT: PROBABILITY AND COMBINATORICS. So I apologize in advance if some of the questions I'm going to ask you guys are too easy.
QST: In a box with 10 blocks, 3 of which are red, what is the probability of picking a red block on each of your first two tries? Assume that you do NOT replace the first block after you have picked it.
ANS: I'm aware of the traditional way to solve problems like this (probability trees). By doing so, the answer is 3/10 * 2/9 = 1/15. Pretty straight forward.
Now, I want to also be able to solve this kind of problem with a counting method (combinatorics). So I thought I can solve it like this:
Unfortunately, I get the wrong result (2/15). This is double the OA (1/15). Any idea how to use the combination formula correctly in this scenario?
Total # of favorable outcomes: 2 red block out of three: 3C2=3
Total # of outcomes: any 2 blocks out of 10: 10C2=45
If you are putting in denominator the number of selections of 2 out of 10, you should also put in nominator number of selections of 2 out of 3.
# of selections of any first block out of 10=10C1, # of selection of any second out of 9=9C1=9, total 10C1*9C1=90
# of selections of the first red block out of three=3C1=3, # of selections of second red block out of three=2C1=2, total 3C1*2C1=6.
Hope it helps.
It would be better to post the questions in PS or DS forums to get more and quick replies.
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