Question

From a standard deck of playing cards, 2 cards are drawn without replacement. What is the probability of drawing both hears or both face cards?

answer is 47/442

Answer 1

why are you giving us the answer

Answer 2

I know the answer but I don't know how to get it, the worksheet give us the answer

Answer 3

The total sample space is \(52 \choose 2\)

Answer 4

Each suit has 3 face cards, so the probability of drawing 2 face cards is \(3\times4 \choose 2\)

Answer 5

I mean the number of ways^

Answer 6

The number of ways to chose two hearts is just \(52\div 4 \choose 52\)

Answer 7

The number of ways to draw to face cards that are both hearts is \(3\choose 2\). You need to know this one so that you can account for double counting.

Answer 8

All together, I get \[\Large
\frac{{3\times 4 \choose 2}+{52\div 4 \choose 2} - {3\choose 2}}{52 \choose 2}
\]

Answer 9

http://www.wolframalpha.com/input/?i=%7B%7B3%5Ctimes+4+%5Cchoose+2%7D%2B%7B52%5Cdiv+4+%5Cchoose+2%7D+-+%7B3%5Cchoose+2%7D%7D%2F%7B52+%5Cchoose+2%7D

\[\Large
\frac{{3\times 4 \choose 2}+{52\div 4 \choose 2} - {3\choose 2}}{52 \choose 2} = \frac{47}{442}
\]