Question

A card is drawn at random from a pack of $52$ cards. The probability that the drawn card is a court card i.e., a jack, queen or a king is

• A. $\frac{3}{52}$
• B. $\frac{3}{13}$
• C. $\frac{4}{13}$
• D. None of these

Answer 1

The correct option is B

$\frac{3}{13}$

Explanation for the correct options:

Finding the probability that the drawn card is a court card

Total number of cards in a pack $=52$ cards

Court card means a jack, queen, or a king

In a pack of well-shuffled cards, we have $4$ king cards, $4$ queen cards, and $4$ queen cards.

Probability $\mathbf{=}\frac{\mathbf{Number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{favorable}\mathbf{}\mathbf{outcomes}}{\mathbf{Total}\mathbf{}\mathbf{number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{favorable}\mathbf{}\mathbf{outcomes}}$

According to the question,

The number of favorable outcomes $=$ $4$king cards, $4$ queen cards, and $4$ queen cards.

The number of favorable outcomes $=12$

Total number of favorable outcomes $=52$

Substituting the values in the formula of probability

Probability $=\frac{12}{52}$

$=\frac{3}{13}$

Hence, option (B) is the correct answer