A single card is drawn from a standard deck of cards. Find the probability if the given information is known about the chosen card. A face card is a jack, queen, or king.

Question

dangerousjesse · Answer

Do you know how many cards are in a deck?

kirbykirby · Answer

A deck usually has 52 cards. And there are 4 suites in a deck: hearts, clubs, diamonds, spades

There is one Jack for every suite, so there are 4 in total. So P(Jack) = 4/12. Finding P(Queen) and P(King) should be obvious to find now. 

We want though the probability: P(Jack OR Queen OR King)
By the inclusion-exclusion principle, using J, Q and K as abbreviations:
$$P(J \cup Q \cup K)\=P(J)+P(Q)+P(K)-P(J \cap Q)-P(J \cap K)-P(Q \cap K)+P(J \cap Q \cap K) $$
But the event of having 2 (or more) face cards at the same time is mutually exclusive, so all the intersection events above have probability 0. And so your problem reduces to finding:$$P(J \cup Q \cup K)=P(J)+P(Q)+P(K)$$

kirbykirby · Answer

Maybe I should rephrase my last paragraph, to be more precise; The event that one card has 2 faces on it cannot happen, so the event of having 2 faces (or more) on one card are mutually exclusive, so the intersection events have probability 0.