All three face cards of spades are removed from a well-shuffled pack of $52$ cards. A card is then drawn at random from the remaining pack. Find the probability of getting ‘ $9$ ’ of black colour?

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Solution

Total number of cards $= 52 - 3 = 49$ . [since $3$ face cards of spade are removed]
So the number of possible outcomes $= 49.$
Let E be the event of getting ‘ $9$ ’ of black colour.
There will be $2$ such cards.
Number of favourable outcomes $= 2$
$P (E) = \frac{N u m b e r o f f a v o u r a b l e o u t c o m e s}{N u m b e r o f p o s s i b l e o u t c o m e s}$
$P (E) = 2 / 49$
Hence the probability of getting ‘09’ of black colour is $2 / 49$ .

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