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 $queen?$

(A) $(i)$ Total number of cards $= 5$.
Total number of queens $= 1$.
$P(\text{getting a queen}) = \frac{\text{Number of favourable outcomes}}{\text{Number of total possible outcomes}} = \frac{1}{5}$.
$(ii)$ When the queen is drawn and put aside,the total number of remaining cards will be $4$.
$(a)$ Total number of aces $= 1$.
$P(\text{getting an ace}) = \frac{1}{4}$.
$(b)$ As the queen is already drawn,the number of remaining queens is $0$.
$P(\text{getting a queen}) = \frac{0}{4} = 0$.