I have used some basic inferential statistics at work but have not really done much on probability before. (School was a long time ago!) I was wondering if someone could help me with the following:

I have 2 normal decks of cards. I pull out 6 cards at random from the first deck and then pull out 6 cards at random from the second deck.

I wanted to know two things.

1) What the probability is of one of the six cards drawn from deck B being a match with one of the six cards drawn from deck A.

2) What the probability is of two of the six cards drawn from deck B being a match with two of the cards drawn from deck A

I calculated the first problem by working out the probability of not having a match and then subtracting it from 1. i.e for the first card drawn from deck B there is 46 in 52 chance that the card wont match, for the second card drawn there will be a 45 in 51 chance (as there is now one less card in the deck.) and so on.

Eg 46/52 x 45/51 x 44/50 x 43/49 x 42/48 x 41/47 = .46 therefore 1-.46 = .54. Hence the probability of having one card match is 54%

Although I think this is correct, I can’t quite figure out how to go about working out the second problem.

Can anyone give me a point in the right direction please.

Cheers