Probability cards

[Math1100]

Hi for this question, “If two cards are drawn from a deck of cards calculate the probability that (a) they are both spades and (b) they both belong to the same suit. (a deck of cards consists of 52 cards each one of which belongs to one of four suits. The number of cards in each of these suits is equal to 13) “.
for this question I thought you would just do (13/52*12/52) but that is wrong .
can someone explain to me the solution

 

[Deleted member 4993]

Hi for this question, “If two cards are drawn from a deck of cards calculate the probability that (a) they are both spades and (b) they both belong to the same suit. (a deck of cards consists of 52 cards each one of which belongs to one of four suits. The number of cards in each of these suits is equal to 13) “.
for this question I thought you would just do (13/52*12/52) but that is wrong .
can someone explain to me the solution

How many ways can you choose (any) 2 cards from a 52 card deck?

 

[Steven G]

... and out of the different ways you can choose 2 cards from 25, how many of them are of the type you want. As also, divide the two results.

One reason your result must be wrong is because when you pick the 2nd card you are not picking from 52 cards as you already chose one already!

 

[Math1100]

Thank you

 

[pka]

Hi for this question, “If two cards are drawn from a deck of cards calculate the probability that (a) they are both spades and (b) they both belong to the same suit. (a deck of cards consists of 52 cards each one of which belongs to one of four suits. The number of cards in each of these suits is equal to 13) “.
for this question I thought you would just do (13/52*12/52) but that is wrong .
can someone explain to me the solution

The only thing wrong is the second \(\color{red}52\) (see above)
it should be: \(\large\dfrac{13}{52}\cdot\dfrac{12}{51}=\dfrac{1}{17}\)