A card is drawn at random from a well shuffled pack of 52 cards. The probability that it is black card or…
A card is drawn at random from a well shuffled pack of 52 cards. The probability that it is black card or face card is
$\frac{3}{13}$
$\frac{5}{13}$
$\frac{6}{13}$
$\frac{8}{13}$
Solution
Here, $\mathrm{n}(\mathrm{S})=52$
Let event A : A black card is drawn. event $B$ : A face card is drawn.
$n(A)=26, n(B)=12, n(A \cap B)=6$
Required probability
$\begin{aligned}
& =P(A \cup B) \\
& =P(A)+P(B)-P(A \cap B) \\
& =\frac{26}{52}+\frac{12}{52}-\frac{6}{52} \\
& =\frac{32}{52}=\frac{8}{13}
\end{aligned}$