A card is drawn from a deck of 52 cards is given.
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-
By using the formula,
P (E) = favourable outcomes / total possible outcomes
= n (E) / n (S)
Where, n (E) = numbers of elements in event set E
And n (S) = numbers of elements in sample space.
Hence,
P (S) = n (spade) / total number of cards
= 13 / 52
= 1/4
P (K) = 4/52
= 1/13
And P (S ⋂ K) = 1/52
We need to find the probability of card being spade or king, i.e.
P (Spade ‘or’ King) = P(S ∪ K)
So, 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)
So, P (S ∪ K) = P (S) + P (K) – P (S ∩ K)
= 1/4 + 1/13 – 1/52
= 17/52 – 1/52
= 16/52
= 4/13
∴ P (S ∪ K) = 4/13