When a card is selected from a standard deck, what is the probability of getting a six and a spade?

1 Answer
Feb 4, 2017

#:. P("6 of spades") = 1/52#


#getting a 6 AND a spade"

The keyword here is "AND". The card that is chosen needs to be both a 6 AND a spade. There is only one card that satisfies both conditions, the 6 of spades.

There are 52 cards in a standard pack.

#:. P("6 of spades") = 1/52#

Compare this to the question: "getting a 6 OR a spade"

There are four 6s in a pack and 13 spades.
However, the 6 of spades is counted under both, so has been counted twice.

There are #13+4-1 =16# cards which will satisfy one of the two conditions.

#:. P("6 or a spade") = 16/52 = 4/13#