Question

A card is drawn randomly from a well shuffled pack of $52$ cards. Find the probability of getting a red card or a black king or a club with an even number

Answer 1

Let $A$ be the event of getting a red card.
$n\left(A\right)=13diamonds+13hearts=26$
Let $B$ be the event of getting a black king.
$n\left(B\right)=1\left(spadeking\right)+1\left(clubking\right)=2$
Let $C$ be the event of getting a club with an even number.
$n\left(C\right)=5$ club cards with numbers $2,4,6,8,10$
$\therefore P\left(A\right)=\frac{26}{52}P\left(B\right)=\frac{2}{52}P\left(C\right)=\frac{5}{52}$
Now, $A,B$ and $C$ are mutually exclusive events.
$\therefore P(A\cup B\cup C)=P\left(A\right)+P\left(B\right)+P\left(C\right)$
$P(A\cup B\cup C)=\frac{26}{52}+\frac{2}{52}+\frac{5}{52}\therefore P(A\cup B\cup C)=\frac{26+2+5}{52}=\frac{33}{52}$
$\therefore$ the probability of getting a red card or a black king or a clubs with an even number is $\frac{33}{52}$