All the 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

(i) a black face card

(ii) a queen

(iii) a black card

(iv) a heart

(v) a spade

(vi) '9' of black colour.

3 face cards of spades are removed, hence total cards = 52 - 3 = 49.

Well-shuffling ensures equally likely outcomes.

Total number of outcomes = 49.

(i) Since 2 suits are of black colour and each suit has 3 face cards but since spades of black colour are removed.

∴ No. of black face cards = 3.

∴ The number of favourable outcomes to the event 'a black face card' = 3.

∴ P(a black face card) = $\dfrac{3}{49}$.

Hence, the probability of drawing a black face card = $\dfrac{3}{49}$.

(ii) Each suit has one queen.

Since, face cards of spades are removed hence, it has no queen.

So, there are 3 queens left.

∴ The number of favourable outcomes to the event 'a queen' = 3.

∴ P(a queen) = $\dfrac{3}{49}$.

Hence, the probability of drawing a queen = $\dfrac{3}{49}$.

(iii) Total no. of black cards = 26.

Since, spades are of black colour and it's face card are removed.

∴ The number of black cards left = 26 - 3 = 23.

∴ The number of favourable outcomes to the event 'a black card' = 23.

∴ P(a black card) = $\dfrac{23}{49}$.

Hence, the probability of drawing a black card = $\dfrac{23}{49}$.

(iv) There are 13 heart cards.

∴ The number of favourable outcomes to the event 'a heart' = 13.

∴ P(a heart) = $\dfrac{13}{49}$.

Hence, the probability of drawing a heart = $\dfrac{13}{49}$.

(v) Since, face cards of spades are removed,

∴ No. of spades left = 13 - 3 = 10.

∴ P(a spade) = $\dfrac{10}{49}$.

Hence, the probability of drawing a spade = $\dfrac{10}{49}$.

(vi) There are 2, '9' numbered cards of black colour.

∴ P(a '9' of black colour) = $\dfrac{2}{49}$.

Hence, the probability of drawing a '9' of black colour = $\dfrac{2}{49}$.