Question

A card is drawn from a pack of 52 cards. Find the probability of getting a king or a heart or a red card.
$\left[3\right]$

Answer 1

Let A be the event of getting a king card. n(A) =4

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

Let B be the event of getting a heart card. n(B) =13

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

Let C be the event of getting a red card. n(C) =26

$P\left(C\right)=\frac{n\left(C\right)}{n\left(S\right)}=\frac{26}{52}$

$\left[1\right]$

P (A Ո B) = P (getting heart king) = 1/52

P (B ՈC) = P (getting red and heart)) = 13/52

P (A ՈC) = P (getting red king) = 2/52

P (A Ո B ՈC) = P (getting heart, king which is red) = 1/52

Therefore, required probability is

P (A U B UC) = P (A) + P (B) + P (C) − P (A ∩ B ) − P(B ∩C) −P (C ∩ A) + P(A ∩ B ∩C)

$\frac{4}{52}+\frac{13}{52}+\frac{26}{52}-\frac{1}{52}-\frac{13}{52}-\frac{2}{52}+\frac{1}{52}=\frac{28}{52}=\frac{7}{13}$

$\left[2\right]$