Question

From a well-shuffled pack of $52$ cards, a card is drawn. The probability of drawing a king is , and the probability of drawing a black $10$ is .

• A. $\frac{1}{13}$
• B. $\frac{2}{13}$
• C. $\frac{1}{52}$
• D. $\frac{1}{26}$
• E. $\frac{3}{13}$

Answer 1

Answer: (A), (D)

$\frac{1}{26}$

Total number of possible outcomes= Total number of cards in the well-suffled deck= $52$

In each of the four suits, their is a king. Threfore, total number of kings in the deck= $1\times 4=4$.

Now, for $\text{P (king)}$, number of favorable outcomes= number of kings in the deck= $4$.

$\therefore \text{P (king)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

$\Rightarrow \text{P (king)}=\frac{\text{Number of kings in the deck}}{\text{Total number of cards}}$

$\Rightarrow \text{P (king)}=\frac{4}{52}=\frac{4\times 1}{4\times 13}=\frac{1}{13}$

$\therefore$ The probability of drawing a king card from a deck of $52$ cards is $\frac{1}{13}$.
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There is only one $10$ numbered card in each of the four suits. And, there are total $2$ black suits (clubs and spades) in a deck of cards. Threfore, $10$ numbered black cards in a deck of cards= $1\times 2=2$.

Now, for $\text{P (black}10\text{)}$, number of favorable outcomes= total number of black $10$ cards= $2$

$\therefore \text{P (black}10\text{)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

$\Rightarrow \text{P (black}10\text{)}=\frac{\text{Total number of black 10 cards}}{\text{Total number of cards}}$

$\Rightarrow \text{P (black}10\text{)}=\frac{2}{52}=\frac{2\times 1}{2\times 26}=\frac{1}{26}$

$\therefore$ The probability of drawing a black $10$ card from a deck of $52$ cards is $\frac{1}{26}$.