Question

A card is drawn from a well-shuffled deck of playing cards. Find the probability of drawing a face card.
A. \[\dfrac{8}{{13}}\]
B. \[\dfrac{3}{{13}}\]
C. \[\dfrac{4}{{13}}\]
D. \[\dfrac{1}{4}\]

Answer 1

Hint: A deck is a 52 card consisting of 4 suites, each suite consists of 13 cards. Each suite has one king, one Queen, one Jack, and one Ace. Other 9 cards will be numbers from 0 to 9. According to this calculation, each suite consists of 4 faces, and then the total deck of 52 cards consists of 12 faces.

Complete step-by-step answer:
Number of cards in a deck is \[x = 52\]
Number of suites in a deck is \[y = 4\]
Number of cards in each suit is \[z = 13\]
Number of faces in each suit is \[p = 3\]
So the total number of faces in a deck that has 52 cards consists of 4 suits \[ \times \]3 faces give 12 faces.
\[4 \times 3 = 12\]
The equation to find the probability of drawing a face card from a deck of 52 cards is
The probability is defined as the ratio of the number of outcomes to the total number of trails, and then the equation can be framed as
\[P = \dfrac{p}{x}\]
Substituting the values in the above equation, then
\[\begin{array}
P = \dfrac{p}{x}\\
 = \dfrac{{12}}{{52}}\\
 = \dfrac{3}{{13}}
\end{array}\]
Therefore, the probability of getting a face card from a deck is \[\dfrac{3}{{13}}\], it means the correct option is (B)
So, the correct answer is “Option B”.

Note: To solve this solution, we have to be clear about what is a deck? And what are the cards a deck consists of? We should know what actually a face card looks like. To solve this solution, we have to come to know the clear definition of the probability. While solving the problem, it should be noted that the number of outcomes should be placed in the numerator and the total trials are placed in the denominator.