Question

what is the probability of drawing P(Jack) in a standard set of cards? P(Spade)? P(Jack of spades)? P(not spade)?

Answer 1

There are 4 suits (hearts, diamonds, spades, clubs) in a deck. And there is one Jack for every suit (so 4 Jacks in total) Since a normal deck has 52 cars, then P(Jack) = 4/52
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For P(Spade), notice that one quarter of the deck consists of spades... so P(spade) = \(\dfrac{52\div4}{52}\)
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\(P(\text{Jack or Spade})=P(\text{Jack})+P(\text{Spade})-P(\text{Jack and Spade})\)
(by the rule for unions)

Now P(Jack and Spade) consists of the cards that are Both a Jack and a Spade. Can you figure out how many this is?
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\(P(\text{not Spade)}=1-P(\text{Spade})\)
(by the rule for complements)