Solution:

Let’s say there are spade cards among the five drawn cards.

Because we can see that the cards are being drawn with replacement, the trials will be Bernoulli trials.

We now know that there are 13 spade cards in a deck of 52 cards.

As a result, the probability of drawing a spade from a 52-card deck

Thus, has a binomial distribution with and

Thus, , where

(i) Probability of drawing all five cards as spades

B

(ii) Probability of drawing three out five cards as spades

(iii) Probability of drawing all five cards as non-spades