Question

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. Select the correct answer from above options

Answer 1

Given: 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- 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