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

Feb 4, 2017

$\therefore P \left(\text{6 of spades}\right) = \frac{1}{52}$

#### Explanation:

#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.

$\therefore P \left(\text{6 of spades}\right) = \frac{1}{52}$

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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.

$\therefore P \left(\text{6 or a spade}\right) = \frac{16}{52} = \frac{4}{13}$