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All face cards of spades are removed from a pack of $52$ playing cards and the remaining pack is shuffled well. A card is then drawn at random from the remaining pack. Find the probability of getting :
(a) a face card
(b) an ace or a jack
(a) a face card
(b) an ace or a jack
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Sol. After removing face cards of spades, total number of cards $$\begin{aligned}& = 52 - 3 = 49 \\ & (a) P(\text{a face card}) = \frac{9}{49} \\ & (b) P(\text{an ace or a jack}) = \frac{7}{49} \text{ or } \frac{1}{7}\end{aligned}$$