A card is then drawn at random from the remaining pack.

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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

Solution:

In a pack of 52 cards
All the three face cards of spade are = 3
Number of remaining cards = 52 – 3 = 49
One card is drawn at random
(i) Probability of a black face card which are = 6 – 3 = 3
Probability = \\ \frac { 3 }{ 49 }
(ii) Probability of being a queen which are 4 – 1 = 3
Probability = \\ \frac { 3 }{ 49 }
(iii) Probability of being a black card = (26 – 3 = 23)
Probability = \\ \frac { 23 }{ 49 }
(iv) Probability of being a heart = \\ \frac { 13 }{ 49 }
(v) Probability of being a spade = (13 – 3 = 10)
Probability = \\ \frac { 10 }{ 49 }
(vi) Probability of being 9 of black colour (which are 2) = \\ \frac { 2 }{ 49 }

From a pack of 52 cards, a blackjack, a red queen and two black kings fell down. A card was then drawn from the remaining pack at random. Find the probability that the card drawn is
(i) a black card
(ii) a king
(iii) a red queen.

Solution:

In a pack of 52 cards, a blackjack, a red queen, two black being felt down.
Then number of total out comes = 52 – (1 + 1 + 2) = 48
(i) Probability of a black card (which are 26 – 3 = 23) = \\ \frac { 23 }{ 48 }
(ii) Probability of a being (4 – 2 = 2) = \\ \frac { 2 }{ 48 } = \\ \frac { 1 }{ 24 }
(iii) Probability of a red queen = (2 – 1 = 1) = \\ \frac { 1 }{ 48 }

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