Question

The face-down deck of cards contains four hearts six diamonds three clubs and six spades. What is the probability that the first two cards drawn will both be spades?

Answer 1

`5/57`

Explanation:

First we need to know how many cards are in the deck. Since we have 4 hearts, 6 diamonds, 3 clubs, and 6 spades, there are `4+6+3+6=19` cards in the deck.

Now, the probability that the first card is a spade is `6/19`, because there are `6` spades out of a deck of `19` cards total.

If the first two cards drawn will be spades, then after drawing one spade we will have `5` left - and since we took a card out of the deck, we will have `18` cards total. That means the probability of drawing a second spade is `5/18`.

To wrap it up, the probability of drawing a spade first (`6/19`) and second (`5/18`) is the product of these:
`P("Drawing two spades")=6/19*5/18=5/57`