Question

A card is drawn from a pack of cards. What is the probability that the drawn card is neither a heart not a king

• A. $\frac{4}{13}$
• B. $\frac{9}{13}$
• C. $\frac{1}{4}$
• D. $\frac{13}{26}$

Answer 1

The correct option is B

$\frac{9}{13}$

Explanation for the correct option:

Step 1. Let $H$ be the event of picking a heart in a deck and $K$ be the event of picking kings in a deck.

Total number of cards in a deck $=52$

Number of hearts in a deck $=13$

$\therefore$$\begin{array}{rcl}P\left(H\right)& =& \frac{13}{52}\\ & =& \frac{1}{4}\end{array}$

Number of kings in a deck $=4$

$\therefore$$\begin{array}{rcl}P\left(K\right)& =& \frac{4}{52}\\ & =& \frac{1}{13}\end{array}$

Step 2. The probability of getting neither heart nor king

Now, there should be a king of heart is common in both king and heart cards. we have to subtract it from the total probability.

The probability of getting either heart or king$=\frac{1}{4}+\frac{1}{13}-\frac{1}{52}$

$=\frac{16}{52}$

$\therefore$The probability of getting neither heart nor king $=1-\frac{16}{52}$

$$\begin{gathered} =\frac{52-16}{52} \\ =\frac{36}{52} \\ =\mathbf{}\frac{\mathbf{9}}{\mathbf{13}} \end{gathered}$$

Hence, Option ‘B’ is Correct.