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# 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 numbers of cards = 5

$$P(E) \ = \ \frac{Number \ of \ favourable \ outcomes}{Total \ number \ of \ outcomes}$$

(i) Numbers of queen = 1

P (picking a queen) $$= \ \frac{1}{5} \ = \ 0.2$$

(ii) If the queen is drawn and put aside, the total numbers of cards left is (5-1) = 4

(a) Total numbers of ace = 1

P (picking an ace) $$= \ \frac{1}{4} \ = \ 0.25$$

(b) Total numbers of queen = 0

P (picking a queen) $$= \ \frac{0}{4} \ = \ 0$$