Seven cards : the eight, the nine, the ten, jack, queen, king and ace of diamonds are well shuffled. One card is then picked up at random.

(i) What is the probability that the card drawn is the eight or the king ?

(ii) If the king is drawn and put aside, what is the probability that the second card picked up is :

(a) an ace ?

(b) a king ?

There are seven cards.

∴ No. of possible outcomes = 7.

(i) No. of favourable outcomes (of getting a eight or the king) = 2.

P(drawing an eight or the king) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{2}{7}$.

Hence, the probability that the card drawn is the eight or the king = $\dfrac{2}{7}$.

(ii) Since, king is drawn and put aside so, no. of cards left = 7 - 1 = 6.

∴ No. of possible outcomes = 6.

(a) No. of favourable outcomes (of getting an ace) = 1.

P(drawing an ace) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{1}{6}$.

Hence, the probability that the card drawn is an ace = $\dfrac{1}{6}$.

(b) Since, king is drawn aside.

∴ No. of favourable outcomes (of getting a king) = 0.

P(drawing a king) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{0}{6}$ = 0.

Hence, the probability that the card drawn is a king = 0.