Question

A card is drawn from a well-shuffled deck of playing cards. What is the probability of drawing a red face card?
A. $\dfrac{4}{{13}}$
B. $\dfrac{7}{{13}}$
C. $\dfrac{8}{{13}}$
D. $\dfrac{3}{{26}}$

Answer 1

To solve this question, we need to have a basic idea of a well-shuffled deck of cards. We need to know how many cards are present and what types of cards are present in a well-shuffled deck of cards. There are four suits, two of red color and two of black. Face cards have a person’s face on them. After that, we need to use the definition of probability, which is the ratio of favorable outcomes to total outcomes.

Complete step-by-step solution:
We know that there will be 52 cards in a well-shuffled deck of playing cards. The well-shuffled pack of playing cards are divided into two suits. One suit consists of red color playing cards. Another suit consists of black color playing cards. The red color cards consist of hearts and diamonds. Whereas the black color cards consist of spades and clubs. In black color cards, we will have 13 spades and 13 clubs. In red color cards, we will have 13 hearts and 13 diamonds. In each set of spades, clubs, hearts and diamonds, we will have nine number cards numbered from two to ten and three face cards. In each set of spades, clubs, hearts and diamonds we will have 3 face cards.
As per the question, we needed to draw a red face card from the well-shuffled deck of 52 cards.
We know that in red cards we will have hearts and diamonds. In each set of hearts and diamonds, we will have 3 face cards. In total, we will have 6 face cards in red cards.
So, the total number of ways to pick a red face card is equal to 6.
$\Rightarrow n\left( E \right) = 6$
We know that the total number of cards in a well-shuffled deck is equal to 52.
So, the total number of ways to pick a card is equal to 52.
$\Rightarrow n\left( S \right) = 52$
We know that the ratio of the number of favorable outcomes to the total number of outcomes is defined as a probability.
$P\left( E \right) = \dfrac{{n\left( E \right)}}{{n\left( S \right)}}$
Substitute the values in the formula,
$\Rightarrow P\left( E \right) = \dfrac{6}{{52}}$
Cancel out the common factors,
$\Rightarrow P\left( E \right) = \dfrac{3}{{26}}$

Hence, option (D) is the correct answer.

Note: We should know some extra information which may be used to solve problems based on a well-shuffled deck of 52 cards. We will have 12 face cards in a well-shuffled deck. In these 12 face cards. we will have 4 kings, 4 queens and 4 jacks. Also remember that in each well-shuffled deck of 52 cards, we will have 4 aces. Students might miss the fact that ace is not a face card and this can make the solution wrong.