$\begin{array}{1 1}(A)\;\large\frac{7}{13}\\(B)\;\large\frac{8}{13}\\(C)\;\large\frac{6}{13}\\(D)\;\large\frac{9}{13}\end{array} $

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Total sample space S=52

Probability of getting a king =$\large\frac{4}{52}$

Probability of getting a heart=$\large\frac{13}{52}$

Probability of getting a red card =$\large\frac{26}{52}$

Step 2:

Probability of getting a king or a heart or a red card

$P(K \cup H \cup R)=P(K)+P(H)+P(R)-P(K \cap H \cap R)$

$\Rightarrow \large\frac{4}{52}+\frac{13}{52}+\frac{26}{52}-\big[\frac{2}{52}+\frac{1}{52}+\frac{12}{52}\big]$

$\Rightarrow \large\frac{43}{52}-\frac{15}{52}$

$\Rightarrow \large\frac{28}{52}$

$\Rightarrow \large\frac{7}{13}$

Step 3:

$\therefore$ Probability of getting a king or a heart or a red card is $\large\frac{7}{13}$

Hence (A) is the correct answer.

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