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Questions  >>  CBSE XI  >>  Math  >>  Probability

A card is drawn from a deck of 52 cards.Find the probability of getting a king or a heart or a red card.

$\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} $

1 Answer

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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