Five cards − the ten, jack, queen, king and ace of diamonds are well shuffled with their faces downwards.
Question:

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

(a) What is the probability that the drawn card is the queeen?
(b) If the queen is drawn and put aside and a second card is drawn, find the probability that the second card is (i) an ace, (ii) a queen.

Solution:

Total number of cards = 5.

(a) Number of queens = 1.

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

$=\frac{1}{5}$

Thus, the probability that the drawn card is the queen is $\frac{1}{5}$.

(b) When the queen is put aside, number of remaining cards = 4.

(i) Number of aces = 1.

$\therefore \mathrm{P}($ getting an ace $)=\frac{\text { Number of favourable outcomes }}{\text { Number of all possible outcomes }}$

$=\frac{1}{4}$

Thus, the probability that the drawn card is an ace is $\frac{1}{4}$.

(ii) Number of queens = 0.

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

$=\frac{0}{4}=0$

Thus, the probability that the drawn card is a queen is 0.