Question

A card is drawn at random from a well shuffled pack of 52 cards.Find the probability that the card drawn is :

(i) a diamond card or a king.

Answer 1

Total number of cards = 52
∴ n (S) = 52
Let A be the event of drawing a diamond card and B be the event of drawing a card of king.
We know:
Number of diamond cards = 13
$\therefore$ n (A) = 13
Number of kings = 4
$\therefore$ n (B) = 4
And,
Number of cards that are diamond and king = 1
$\therefore$ n (A $\cap$ B) = 1

P (A) = $\frac{n\left(A\right)}{n\left(S\right)}=\frac{13}{52}=\frac{1}{4}$

P (B) = $\frac{n\left(B\right)}{n\left(S\right)}=\frac{4}{52}=\frac{1}{13}$

And,
P (A $\cap$ B) = $\frac{n(A\cap B)}{n\left(S\right)}=\frac{1}{52}$

Now, on applying the addition theorem of probability, we get:
P(A $\cup$ B) = P(A) + P(B) $-$ P(A $\cap$ B)

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

$\therefore$ Probability of drawing a diamond card or a king = $\frac{4}{13}$