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probability

by sgr21 » Mon Nov 04, 2013 12:05 am
From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being queens?
(A) 1/52
(B) 1/4
(C) 3/221
(D)1/221
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by theCodeToGMAT » Mon Nov 04, 2013 12:46 am
There are 4 queens in total..

So, 4/52 * 3/51 = 1/13 * 1/17 = 1/221
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by Brent@GMATPrepNow » Mon Nov 04, 2013 7:39 am
sgr21 wrote:From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being queens?
(A) 1/52
(B) 1/4
(C) 3/221
(D)1/221
theCodeToGMAT's approach uses probability rules, and it's the approach that I'd probably take too.
However, I just wanted to show that we can also solve the question using counting techniques.

P(both queens) = (# of outcomes with 2 queens)/(total # of 2-card outcomes)

# of outcomes with 2 queens
There are 4 queens in a deck of cards.
Since the order of the 2 selected cards does not matter (e.g. selecting queen of clubs and then queen of hearts is the same as selecting queen of hearts and then queen of clubs), we can use combinations.
We can select 2 queens from 4 queens in 4C2 ways ( = 6 ways)

Aside: If anyone is interested, we have a free video on calculating combinations (like 4C2) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789

total # of 2-card outcomes
There are 52 in a deck of cards.
Since the order of the 2 selected cards does not matter, we can use combinations.
We can select 2 cards from 52 cards in 52C2 ways ( = 26x51 ways )

So, P(2 queens) = 6/(26 x 51)
= [spoiler]1/221[/spoiler]
= D

Cheers,
Brent
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by Brent@GMATPrepNow » Mon Nov 04, 2013 7:45 am
By the way, in its current form, this could never be an official GMAT question because it is culturally biased. A GMAT question would never require test-takers to know the composition of a deck of cards since not all cultures play cards.

Cheers,
Brent
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