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

Question

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

Vedantu Content Team · Accepted Answer

$    \  {	ext{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}}{	ext{.}}   \  {	ext{Remaining card in the bundle after removing 6 black face cards}}{	ext{.}}   \   \Rightarrow {	ext{52 - 6 = 46}}   \  {	ext{(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}}{	ext{.}}   \  {	ext{  }}p({	ext{red face card) = }}\dfrac{{{	ext{favorable outcome}}}}{{{	ext{total no of outcome}}}} = \dfrac{6}{{46}} = \dfrac{3}{{23}}   \  ({	ext{ii) Favorable outcome of red card =  we know that there are 26 red cards , and all the red cards in the deck }}{	ext{.}}   \  {	ext{  }}p({	ext{red card) =  }}\dfrac{{{	ext{favorable outcome}}}}{{{	ext{total no of outcome}}}} = \dfrac{{26}}{{46}} = \dfrac{{13}}{{23}}   \  ({	ext{iii) Favorable outcome of black card =  we know that there are 26 black cards in which 6 black face cards are removed}}   \  {	ext{                                       }}	herefore {	ext{Remaining black cards  = 26 - 6 = 20}}   \  p({	ext{black card) = }}\dfrac{{{	ext{favorable outcome}}}}{{{	ext{total no of outcome}}}} = \dfrac{{20}}{{46}} = \dfrac{{10}}{{23}}   \  {	ext{(iv) favorable outcome of a king =  there are 4 kings in a deck of a card in which we remove 2 cards }}   \  {	ext{                                         }}	herefore {	ext{Remaining kings = 4 - 2 = 2}}   \  p(king) = \dfrac{{{	ext{favorable outcome}}}}{{{	ext{total no of outcome}}}} = \dfrac{2}{{46}} = \dfrac{1}{{23}}   \  {	ext{Note: -  For solving the question of probability , first of all we have to find favorable outcome and then divide it }}   \  {	ext{          by total no of outcome to get the probability}}{	ext{.}}   \ $

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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}} \\ $

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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}} \\
$