Question

From a pack of $52$ playing cards, jack, queens, kings, and aces of red color are removed. From the remaining, a card is drawn at random. Find the probability that the card drawn is a black queen, a red card, a black jack, a picture card (jacks, queens, and kings are picture cards).

Answer 1

Step 1: Use the formula for probability:

$P\left(E\right)=\frac{Numberoffavourableoutcomes}{Totalnumberofpossibleoutcomes}$

Step 2: Find the probability of the card drawn is a black queen:

The total number of cards in a pack $=52$

After removing the red-colored - jack, queen, king, and aces,

Number of cards $=52-8=44$

Number of red cards $=26-8=18$

The number of black queens $=2$

Let $E$ be the even of getting a black queen from the pack

We know that, probability

$$\begin{gathered} P\left(E\right)=\frac{2}{44} \\ =\frac{1}{22} \end{gathered}$$

Step 3: Find the probability of the card drawn is a red card:

The number of red cards after removing the red-colored - jack, queen, king, and aces,$=18$

Let $E$ be the even of getting a red card from the pack

We know that, probability,

$$\begin{gathered} P\left(E\right)=\frac{18}{44} \\ =\frac{9}{22} \end{gathered}$$

Step 4: Find the probability of the card drawn is a black jack:

Number of blackjack cards $=2$

Let $E$ be the even of getting blackjack from the pack.

We know that, probability

$$\begin{gathered} P\left(E\right)=\frac{2}{44} \\ =\frac{1}{22} \end{gathered}$$

Step 5: Find the probability of the card drawn is a picture card:

Number of picture cards $=12-6=6$ (as red cards are removed and there are six red picture cards)

Let $E$ be the even of getting a a picture card from the pack

We know that, probability

$$\begin{gathered} P\left(E\right)=\frac{6}{44} \\ =\frac{3}{22} \end{gathered}$$

Hence, from the conclusions made, the probability of the card drawn being a black queen is $\frac{1}{22}$, a red card is $\frac{9}{22}$, a blackjack is $\frac{1}{22}$, and a picture card (jacks, queens, and kings are picture cards) is $\frac{3}{22}$