Question

All kings, jacks and diamonds have been removed from a pack of $52$ playing cards and the remaining cards are well shuffled. A card is drawn from the remaining pack. Find the probability that the card drawn is: a red queen, a face card, a black card, a heart.

Answer 1

Step 1: Use the Formula of probability:

$P\left(A\right)=\frac{\text{number of outcome favourable to A}}{\text{total number of possible outcome}}$

or

$P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}$

Where,

• $P\left(A\right)$ is the probability of an event$\text{'}A\text{'}$
• $n\left(A\right)$ is the favorable outcomes of the event ‘$\text{'}A\text{'}$’
• $n\left(S\right)$ is total number of possible outcomes in a sample space

Step 2: The probability to getting a red queen card:

The total number of cards are $52$ and all kings, jacks and diamonds cards are removed. Removed cards,$\left\{K,D,J\right\}$(i.e) $4+4+11=19$.

Then the remaining cards are$n\left(S\right)=52-19=33$

S is a sample space of all possible outcomes which is $33$ cards.

Thus, the total number of possible outcome in a sample space is,$n\left(S\right)=33$

Let, A be the event of “getting a red queen card”

In a deck of $52$ cards, the total number of red cards are $26$. But, Diamond $13$cards are removed from the deck of $52$cards.

Then the remaining cards are $13$. So, the favorable outcomes of getting a red queen card, we get $n\left(A\right)=1$

$P\left(A\right)=\frac{1}{33}$

Step 3: The probability to getting a face card:

Let, A be the event of “getting a face card”

The face cards are king, queen and jack. But, All kings, jacks and diamonds cards are removed from a deck of $52$cards.

So, the remaining card is Queen. So, the favorable outcomes of getting a face card, we get $n\left(A\right)=3$

$P\left(A\right)=\frac{3}{33}=\frac{1}{11}$

Step 4: The probability to getting a black card:

Let, A be the event of “getting a black card”

The total number of black cards are $26$. But, All kings, jacks and diamonds cards are removed from a deck of $52$ cards.

In black cards, the king $2$cards and jack $2$ cards removed. So, the remaining card is $22$. Then, the favorable outcomes of getting a black card, we get $n\left(A\right)=22$

$P\left(A\right)=\frac{22}{33}=\frac{2}{3}$

Step 5: The probability to getting a heart card:

Let, A be the event of “getting a heart card”

The total number of hear cards are $13$. But, All kings, jacks and diamonds cards are removed from a deck of $52$ cards.

In heart cards, the king $1$ card and jack $1$ card removed. So, the remaining card is $11$. Then, the favorable outcomes of getting a heart card, we get $n\left(A\right)=11$

$P\left(A\right)=\frac{11}{33}=\frac{1}{3}$

Hence, the probability that the card drawn is a red queen $\frac{1}{33}$, a face card$\frac{1}{11}$, a black card$\frac{2}{3}$, a heart$\frac{1}{3}$