Question

One card is selected at random from a standard 52-card deck of playing cards. What is the probability that the card selected is not a spade?

Answer 1

`12/13`

Explanation:

In a standard 52-card deck, there are 4 Aces. We can figure out the probability of drawing a card that isn't a spade in two ways:

Directly

There are four 2s, four 3s,... all the way up to 4 Kings (12 ordinal cards in all, with each ordinal having four suits), and so we can say:

`"the sum of 12 ordinal cards with 4 suits to each ordinal"/"all possible cards"`

which works out to be

`(4xx12)/52=48/52=12/13`

Indirectly

We can also do this by saying that there are 4 cards we don't want from a collection of 52, and so:

`(52-4)/52=48/52=12/13`