Question

A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of its being a spade or a king.

Answer 1

$\because$ 1 card is drawn from a well shuffled deck of 52 cards

$\therefore S={}^{52}{C}_1=52$

Now, the favourable events is that drawn card is either spade or a king

Let A = Event of choosing shade

$\Rightarrow {}^{13}{C}_1=13$

B = Event of choosing a king

$\Rightarrow {}^4{C}_1=4$

Also, king can be of spade

$\therefore (A\cap B)=1$

$\therefore P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

= $\frac{13}{52}+\frac{4}{52}-\frac{1}{52}=\frac{16}{52}=\frac{4}{13}$