Question

A card is drawn from a standard $52$ card deck. What is the probability that the card is a red jack, given that the card is a face card (a jack, queen, or king)?

• A. $\frac{1}{12}$
• B. $\frac{1}{6}$
• C. $\frac{1}{3}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A

$\frac{1}{12}$

The explanation for correct option:

Option (A):

Here, the sample space is face cards.

The number of total outcomes is the number of total face cards $3\times 4=12$.

The number of favorable outcomes is the Number of red jacks$1$. Thus, the probability of one red joke:

$\begin{array}{rcl}\mathrm{Probability}& =& \frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Number}\mathrm{of}\mathrm{total}\mathrm{outcomes}}\\ & =& \frac{1}{12}\end{array}$

The probability that the card is a red jack given card is a face card is $\frac{1}{12}$.

Therefore, Option (A) is the correct option.