Question

A card is drawn from a pack of cards. Find the probability that the card will be queen or a heart

• A. $\frac{4}{3}$
• B. $\frac{16}{3}$
• C. $\frac{4}{13}$
• D. $\frac{5}{3}$

Answer 1

The correct option is C

$\frac{4}{13}$

Explanation for the correct option:

Step 1. Find the probability of getting queen or a heart:

Total number of cards in a deck $=52$

Total number of queens in a deck $=4$

Total number of hearts in a pack $=13$

Number of cards that are either heart or queen $=16$

Number of cards hat are neither heart nor queen $=52-16$

$=36$

Now,

Probability of getting a queen is, $P\left(Q\right)=\frac{4}{52}$

Probability of getting a heart is, $P\left(H\right)=\frac{13}{52}$

Probability of getting queen of heart, $P(Q\cap H)=\frac{1}{52}$

Step 2. The required probability of getting queen or a heart $=P\left(Q\cup H\right)$

$\therefore P(Q\cup H)$$=\frac{4}{52}+\frac{13}{52}-\frac{1}{52}$ $\left[\mathbf{\because }\mathit{P}\mathbf{(}\mathit{A}\mathbf{\cup }\mathit{B}\mathbf{)}\mathbf{}\mathbf{=}\mathbf{}\mathit{P}\mathbf{\left(}\mathit{A}\mathbf{\right)}\mathbf{}\mathbf{+}\mathbf{}\mathit{P}\mathbf{\left(}\mathit{B}\mathbf{\right)}\mathbf{}\mathbf{-}\mathbf{}\mathit{P}\left(A\cap B\right)\right]$

$$\begin{gathered} =\frac{4+13-1}{52} \\ =\frac{16}{52} \\ =\frac{\mathbf{4}}{\mathbf{13}} \end{gathered}$$

Hence, Option ‘C’ is Correct.