A standard deck of 52 playing cards is well shuffled and one card is drawn at random
MATHEMATICS · Subjective · A Level · Mathematics · Probability · Probability
Problem
A standard deck of 52 playing cards is well shuffled and one card is drawn at random. Consider the following events:
A: the card drawn is a face card (J, Q, or K of any suit).
B: the card drawn is a red number card (2 through 10 of hearts or diamonds).
C: the card drawn is a black ace.
(i) Prove that the events A, B and C are pairwise mutually exclusive.
(ii) Determine P(A), P(B) and P(C).
(iii) Find P(A∪B∪C).
(iv) Hence find the probability that the card drawn belongs to none of these three events.