# What is the conditional probability that a card drawn at random from a pack of 52 cards is a face card, given that the drawn card is a spade?

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The formula for the conditional probability of event A happening given that it's known event B already happened is given by the formula:

If we let A = "Drawing a face card" and B = "Drawing a spade", we can compute this by finding two values:

Since there are three face cards (Jack, Queen, and King) in the spades suit, and 52 total possible cards, the

Thus:

**Alternative**

It's easier to do this when you recognize that knowing the drawn card was a spade has "collapsed" the set S of possibilities down to just 13 cards (the spades). Of those 13, only 3 are face cards. Thus:

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