Question

A card is drawn from a well shuffled pack of playing cards. What is the probability that it is either a spade or an ace or both?

Answer 1

Let $A=$ getting a spade
$B=$ getting an ace
$A\cap B=$ getting an ace of spade
$A\cup B=$ getting either a spade or an ace or both $=?$
$P\left(A\right)=\frac{13}{52}=\frac{1}{4},P\left(B\right)=\frac{4}{52}=\frac{1}{13}$
$P(A\cap B)=\frac{1}{52}$

Using addition theorem,
$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$=\frac{1}{4}+\frac{1}{13}-\frac{1}{52}=\frac{16}{52}=\frac{4}{13}$.