Five cards−−the ten, jack, queen, king and ace of diamonds,
Question:

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?

Solution:

(i) Total number of cards = 5

Total number of queens = 1

$P($ getting a queen $)=\frac{\text { Number of favourable outcomes }}{\text { Number of total possible outcomes }}$

$=\frac{1}{5}$\

(ii) When the queen is drawn and put aside, the total number of remaining cards will be 4.

(a) Total number of aces = 1

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

(b) As queen is already drawn, therefore, the number of queens

will be 0

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