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?
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
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: