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# All the black face cards are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a(i) face card(ii) red card(iii) black card(iv) king

Last updated date: 18th Mar 2023
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Hint: In a deck of cards there are 26 black cards and 26 red cards, out of which there are 12 face cards-6 black and 6 red. So before starting the solution remove 6 black face cards from the deck of cards and use the formula

$Probability = \dfrac{{{\text{favorable outcome}}}}{{{\text{total no of outcome}}}}$.

We know that there are 6 black face cards in a deck of cards , 2 king of black , 2 queen of black and 2 jack of black.

Remaining card in the bundle after removing 6 black face cards is

$\Rightarrow {\text{52 - 6 = 46}}$

(i) Favorable outcome of a face card = we know there are 6 red face cards , 2 red king , 2 red queen and 2 red jack.

$p({\text{red face card) = }}\dfrac{{{\text{favorable outcome}}}}{{{\text{total no of outcome}}}} = \dfrac{6}{{46}} = \dfrac{3}{{23}}$

(ii) Favorable outcome of red card = we know that there are 26 red cards , and all the red cards in the deck.

$p({\text{red card) = }}\dfrac{{{\text{favorable outcome}}}}{{{\text{total no of outcome}}}} = \dfrac{{26}}{{46}} = \dfrac{{13}}{{23}}$

(iii) Favorable outcome of black card = we know that there are 26 black cards in which 6 black face cards are removed.

$\therefore$ Remaining black cards = 26 - 6 = 20.

$p({\text{black card) = }}\dfrac{{{\text{favorable outcome}}}}{{{\text{total no of outcome}}}} = \dfrac{{20}}{{46}} = \dfrac{{10}}{{23}}$

(iv) Favorable outcome of a king = there are 4 kings in a deck of a card in which we remove 2 cards.

$\therefore$ Remaining kings = 4 - 2 = 2

$p(king) = \dfrac{{{\text{favorable outcome}}}}{{{\text{total no of outcome}}}} = \dfrac{2}{{46}} = \dfrac{1}{{23}}$

Note: - For solving the question of probability , first we have to find a favorable outcome and then divide it by total no of outcomes to get the probability.