Question

From a deck of $52$ cards, a card is drawn. The probability of drawing a red face card is . The probability that drawn card is black lettered is .

• A. $\frac{3}{26}$
• B. $\frac{3}{13}$
• C. $\frac{4}{13}$
• D. $\frac{2}{13}$
• E. $\frac{5}{26}$

Answer 1

Answer: (A), (D)

$\frac{2}{13}$


In above tree diagram, $52$ playing cards are classified into $4$ suits $\left(\text{2 red and 2 black}\right)$, and each of four suits can further be divided as shown in the diagram below.


As per the above diagrams,

Total number of possible outcomes= Total number of cards= $52$

Number of face cards in one suit= $3$, and we have $2$ red suits (diamonds and hearts). Therefore, total number of red face cards= $3\times 2=6$.

$\therefore$ Number of favorable outcomes= Total number of red face cards= $6$

Now,
$\text{P (drawing red face card)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$
$\Rightarrow \text{P (drawing red face card)}=\frac{\text{Number of red face cards}}{\text{Total number of cards}}$
$\Rightarrow \text{P (drawing red face card)}=\frac{6}{52}=\frac{2\times 3}{2\times 26}=\frac{3}{26}$

$\therefore$ The probability of drawing red face card from a deck of $52$ playing cards is $\frac{3}{26}$.
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As per the above diagram, there are $4$ lettered (J, K, Q, A) cards in one suit, and there are total $2$ black suits (clubs and spades). Therefore, total number of black lettered cards= $4\times 2=8$.

$\therefore$ Number of favorable outcomes= Number of black lettered cards= $8$

Now,
$\text{P (drawing black lettered card)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$
$\Rightarrow \text{P (drawing black lettered card)}=\frac{\text{Number of black lettered cards}}{\text{Total number of cards}}$
$\Rightarrow \text{P (drawing black lettered card)}=\frac{8}{52}=\frac{4\times 2}{4\times 13}=\frac{2}{13}$

$\therefore$ The probability of drawing a black lettered card from a deck of $52$ cards is $\frac{2}{13}$.