Question

What is the probability of drawing a red face card from a pack of 52 playing cards.
A. ${\displaystyle \frac{3}{13}}$
B. ${\displaystyle \frac{1}{13}}$
C. ${\displaystyle \frac{1}{26}}$
D. ${\displaystyle \frac{2}{13}}$

Answer 1

Hint: We first explain the term face cards in terms of playing cards. Then we find the numbers of face cards in a deck. We find the number of ways both conditional and total events can be arranged. Then we find the probability of drawing a red face card from a pack of 52 playing cards.

Complete step-by-step solution:
In a deck of playing cards, the term face card or court card is generally used to describe a card that depicts a person as opposed to the pip cards. They are also known as picture cards.
So, the face cards in a pack of 52 cards are only jack, king and queen. There are 3 types of face cards.
Every face card has 4 types of patterns and they are spades, heart, diamond and club.
It means there are in total $4\times 3=12$ such face cards in 52 playing cards.
We need to find the probability of drawing a red face card from a pack of 52 playing cards.
Let us define the event of drawing a red face card from a pack of 52 playing cards as A and the event of drawing a card from a pack of 52 playing cards as S.
We find the number of ways the events A and S can be arranged.
So, $n\left(A\right)=12$ and $n\left(S\right)=52$.
The probability of drawing a red face card from the pack will be $p\left(A\right)={\displaystyle \frac{n\left(A\right)}{n\left(S\right)}}$.
We place the values and get $p\left(A\right)={\displaystyle \frac{n\left(A\right)}{n\left(S\right)}}={\displaystyle \frac{12}{52}}={\displaystyle \frac{3}{13}}$. The correct option is A.

Note: We need to remember there are two types of things in playing cards. One is colour and the other one is pattern. We know that every type of number card and face cards exist in 4 patterns. Colour divisions are of 2 being red and 2 as black.