Question

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

Answer 1

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