3 cards are drawn from a regular deck of 52 cards, what is the probability that all three cards are spades

Question

 3 cards are drawn from a regular deck of 52 cards, what is the probability that all three cards are spades 

Answer 1

Hi Bridget,

 

There are 13 Spades in the pack of 52 cards

 

P( all 3 Spade cards) = 13

                                  c

                                    3                   = 13!/10!*3!

                              _________                                    = 11*12*13  

                              52                           52!/49!*3!     

                                  c                                                  50*51*52     = 11/850

                                    3                                                                            

Answer 2

Hi Bridget,

 

Probability breaks down to this basic formula:

 

     desired outcome    

total possible outcomes

 

Also, you need to know there are 13 spades in a deck of cards.

 

So, on your first draw, the chances of getting a spade are:

 

13    (desired outcome: pick one of the 13 spades)

52    (total possibilities: 52 cards in the deck)

 

But on your second draw, if you don't replace the card, your chances of getting a spade are:

 

12

51

 

because you only have 12 spades left, and 51 cards total.

Then, on your last draw, the chances of getting a spade are down to:

 

11

50

 

Since each of these probabilities depend on each other, you multiply them up to get your overall probability:

 

13 * 12 * 11 =   1,716

52    51    50    132,600

 

This reduces, or you can just divide to get a decimal.