Five cards—the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. 

(i) What is the probability that the card is the queen? 

(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?

Total number of cards = 5 (ten, jack, queen, king, and ace of diamonds)

We know that, P(E) = (Number of favorable outcomes/ Total number of outcomes)

(i) Numbers of queens = 1

Using formula, 

P (picking a queen) = 1/5 

= 0.2

(ii) If the queen is drawn and put aside, the total number of cards left is (5 - 4) = 4

(a) number of the ace of diamonds = 1

P (picking an ace) = 1/4 

= 0.25

(b) in the new case, the number of queens = 0

P (picking a queen) = 0/4 

= 0