Let X = number of spade cards.
p = probability of drawing a spade card from a pack of 52 cards.
Since there are 13 spade cards in the pack of 52 cards.
The p.m.f. of X is given by
(i) P(all five cards are spade)
Hence, the probability of all the five cards are spades = \(\frac{1}{1024}\)
(ii) P(only 3 cards are spade) = P[X = 3]
Hence, the probability of only 3 cards are spades = \(\frac{45}{512}\)
(iii) P(none of cards is spade) = P[X = 0]
Hence, the probability of none of the cards is a spade = \(\frac{243}{1024}\)