Question

A card is drawn at random from a pack of $52$ playing cards. Find the probability that the card drawn is neither a red card nor a black king.

Answer 1

Hint: Here, in the given question, we are given that a card is drawn at random from a pack of $52$ playing cards and we need to find the probability that the card drawn is neither a red card nor a black king. There are $52$ cards in a deck. The probability of finding a card can be calculated by dividing the number of cards of the given type by the total number of cards.

Complete answer:
As we know,
A deck of cards contains $52$ cards. There are $26$ red cards and $26$ black cards in the deck of cards. Cards of spades and clubs are black cards. Cards of hearts and diamonds are red cards. They are divided into four suits: Spades, diamonds, clubs and hearts each suit has $13$ cards. The cards in each suit are ace, king, queen, jack, $10$, $9$, $8$, $7$, $6$, $5$, $4$, $3$ and $2$.
$P(A)={\displaystyle \frac{N(E)}{N(S)}}$
This is the formula of finding the probability of any event $A$ and $N(E)$ is the number of favorable outcomes and $N(S)$ is total outcomes or sample space.
Here, we need to find the probability that the card drawn is neither a red card nor a black king. That means we need to subtract the total number of red cards and the total number of black king cards from the total number of cards.
Total number of red cards = $26$
Total number of black king cards = $2$ (one king of spade and one king of club)
Therefore, number of favorable outcomes = $52-(26+2)$
$=52-28$
On subtraction, we get
$=24$
$\Rightarrow N(E)=24$
As we know the total number of cards is $52$.
$\Rightarrow N(S)=52$
$P(A)={\displaystyle \frac{N(E)}{N(S)}}$
$\Rightarrow P(A)={\displaystyle \frac{24}{52}}$
Probability of getting neither a red card nor a black king is = ${\displaystyle \frac{24}{52}}$.

Note:
You have to find the total number of outcomes and total number of Favorable outcomes and just put in the formulae of finding the Probability in this type of cards question you should have knowledge of cards distribution. Make sure to not count a card twice. Also remember that an ace is not a face card. Many students make that mistake.
The distribution of a deck of playing cards:
In a pack or deck of $52$ playing cards, they are divided into $4$ suits of $13$ cards each; i.e. spades, hearts, diamonds and clubs. Cards of spades and clubs are black cards. Cards of hearts and diamonds are red cards. The cards in each suit are ace, king, queen, jack or knaves, $10$, $9$, $8$, $7$, $6$, $5$, $4$, $3$ and $2$.