krisraam wrote:Finding the probability of selecting cards that are not pairs.
Probability of selecting first card = 12/12 = 1 ( It can be any card).
Probability of selecting second card = 10/11 ( 11 cards are left for selection. We shouldn't select the matching card. )
Probability of selecting the third card = 8/10 ( 10 cards left we shouldn't select the two cards that match the already selected 2 cards)
Probability of selecting the 4th card = 6/9
Probability of selecting the cards with no pairs = 1* 10/11*8/10*6/9 = 16/33
Probability of selecting at least one pair = 1-16/33 = 17/33.
Thanks
Raama
I
really like the way you solve the problems, makes it look simpler and understandable. I always fight between 2 methods. This is the method that I chose; however, it took more than 2 mins, but less than 4 mins.
P(E): Finding at least 1 pair that have same value.
4 cards chosen from 12: 12C4 ways
We find P(E`): Finding none of the 4 cards chosen have same value
=6C4 * 4C1 * 4 (ie choose 4 cards from a pair of 6 cards, such that, you choose 1 card from each pair and this can be done in 4 ways) / (12C4)
= 16/33
p(E) = 1-P(E`) = 1 - 16/33 = 17/33
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Always do what you're afraid to do. Whoooop GMAT