card question

Question

ASK A QUESTION
You draw two cards from a standard deck without replacement. Determine the probability that:
a. Both are Diamonds.

Answer 1

It looks like you meant to include additional questions, but only "A: slipped in, so I can deliver only on that one. The good news is that the method is easy, and you can certainly manage the missing questions just as easily. 

There are 52 cards in a standard deck, divided into four suits:diamonds, clubs, hearts and spades. That means the 52 cards are divided by 4, giving you 13 diamonds. 

If you pick the first card, you will of course have a probability of 13 / 52 of getting a diamond. However, the second card has fewer diamonds and fewer cards altogether, so the next probability drops to: 12 / 51. Whenever two (or more) events are consecutive, you multiply the results. In your case, that becomes:

 

(13 / 52) * (12 / 51)               Reduce the fractions and you now have:

 

= (1 / 4) * (4 / 17)

= (1 / 1) * (1 / 17)

= 1 / 17

Ta-da! If you sample with replacement, remember to keep the values the same for both the desired card and the deck as a whole.