Question

If you reveal the top two cards of a deck in succession, what are the chances they both have
the same face value (both aces, both kings, etc)?

I have a million more like these :(

Answer 1

would it be 13 choose 1 times something over 52 choose 2?

Answer 2

so, if the first card can be any number the probability shouldnt matter for the first card

Answer 3

after the first card is drawn you're left with 51 cards and 3 chances of picking the same card

Answer 4

so im guessing the answer is 3/51

Answer 5

do you get what im saying?

Answer 6

yeah, thank you!

Answer 7

k

Answer 8

you're welcome

Answer 9

there are 52 cards in a deck and you want to pick 2 cards with the same face value
so lets say i draw 2 cards and i get 2 aces, then thats one possible combo. There are 4 aces and i want to pick 2 of those 4 aces to get what im looking for which can be represented as

\[\left(\begin{matrix}4 \\ 2\end{matrix}\right)\]

notice its not limited to aces but it works for 2, 3, 4 .. king so you need to multiply that by 13

\[13\left(\begin{matrix}4 \\ 2\end{matrix}\right)\]

remember the binomial theorem which you divide by the total attempts
\[\left(\begin{matrix}52 \\ 2\end{matrix}\right)\]
\[\frac{ 13\left(\begin{matrix}4 \\ 2\end{matrix}\right) }{ \left(\begin{matrix}52 \\ 2\end{matrix}\right)}\]


so your answer should be

Answer 10

yay! i was almost right, thank you :)
0.0588?

Answer 11

yea thats what i got