A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of its being a spade or a king.
As a card is drawn from a deck of 52 cards
Let S denotes the event of card being a spade and K denote the event of card being King.
As we know that a deck of 52 cards contains 4 suits (Heart ,Diamond ,Spade and Club) each having 13 cards. The deck has 4 king cards one from each suit.
We know that probability of an event E is given as-
P(E) =
Where n(E) = numbers of elements in event set E
And n(S) = numbers of elements in sample space.
Hence,
P(S) =
P(K) =
And P(S ∩ K) =
We need to find the probability of card being spade or king, i.e.
P(Spade ‘or’ King) = P(S ∪ K)
Note: By definition of P(A or B) under axiomatic approach(also called addition theorem) we know that:
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
∴ P(S ∪ K) = P(S) + P(K) - P(S ∩ K)
⇒ P(S ∪ K) =
∴ P(S ∪ K) = 4/13