Two cards are drawn at random from a pack of cards. What is the probablity that both these cards are of black color or both are aces?
Hi parveen110,
This type of probability question comes with a minor twist to the math: you have 2 black aces, so you have be careful that you don't count those "combos" more than once.
In real basic terms, probability is "the number of ways you want something to happen" divided by the "total number of possibilities."
Since we're dealing with (what I assume is) a 52 card deck, there are a couple of ways to do the "math"....
Assuming order DOES matter, the total number of possible ways to pull two cards is: 52 x 51
The total number of ways of pulling 2 black cards is: 26 x 25
The total number of ways of pulling 2 aces is: 4 x 3
BUT since two aces are black, that "combo" appears in both the "2 black cards" and the "2 aces" calculations. You're NOT allowed to count that combo twice, so you have to subtract the extra iterations.
The total number of ways of pulling 2 black aces is: 2 x 1
So, the final probability is:
[(26)(25) + (4)(3) - (2)(1)] / (52)(51)
This reduces to: 160/ 663
GMAT assassins aren't born, they're made,
Rich
