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
Brent Hanneson - Creator of GMATPrepNow.com
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