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# ${\text{All the black face cards are removed from a pack of 52 cards}}{\text{. }} \\ {\text{The remaining cards are well shuffled and then a card is drawn at random}}{\text{.}} \\ {\text{Find the probability of getting a }} \\ {\text{(i) face card (ii) red card (iii) black card (iv) king}} \\$  Verified
$\\ {\text{We know that there are 6 black face card in a deck of card , 2 king of black , 2 queen of black and 2 jack of black}}{\text{.}} \\ {\text{Remaining card in the bundle after removing 6 black face cards}}{\text{.}} \\ \Rightarrow {\text{52 - 6 = 46}} \\ {\text{(i) Favorable outcome of a face card = we know there are 6 red face cards , 2 red king , 2 red queen and 2 red jack}}{\text{.}} \\ {\text{ }}p({\text{red face card) = }}\dfrac{{{\text{favorable outcome}}}}{{{\text{total no of outcome}}}} = \dfrac{6}{{46}} = \dfrac{3}{{23}} \\ ({\text{ii) Favorable outcome of red card = we know that there are 26 red cards , and all the red cards in the deck }}{\text{.}} \\ {\text{ }}p({\text{red card) = }}\dfrac{{{\text{favorable outcome}}}}{{{\text{total no of outcome}}}} = \dfrac{{26}}{{46}} = \dfrac{{13}}{{23}} \\ ({\text{iii) Favorable outcome of black card = we know that there are 26 black cards in which 6 black face cards are removed}} \\ {\text{ }}\therefore {\text{Remaining black cards = 26 - 6 = 20}} \\ p({\text{black card) = }}\dfrac{{{\text{favorable outcome}}}}{{{\text{total no of outcome}}}} = \dfrac{{20}}{{46}} = \dfrac{{10}}{{23}} \\ {\text{(iv) favorable outcome of a king = there are 4 kings in a deck of a card in which we remove 2 cards }} \\ {\text{ }}\therefore {\text{Remaining kings = 4 - 2 = 2}} \\ p(king) = \dfrac{{{\text{favorable outcome}}}}{{{\text{total no of outcome}}}} = \dfrac{2}{{46}} = \dfrac{1}{{23}} \\ {\text{Note: - For solving the question of probability , first of all we have to find favorable outcome and then divide it }} \\ {\text{ by total no of outcome to get the probability}}{\text{.}} \\$