Question

Red queens and black jacks are removed from a pack of $52$ playing cards.A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the drawn card is
(i) a king
(ii) of red color
(iii) a face card
(iv) a queen

Answer 1

2 red queens and 2 black jacks are removed from a pack of 52 cards.
So, cards remaining are 48.
$\therefore n\left(S\right)=48$
We need to find probability that 1 card drawn at random is
(1) a king
There are 4 kings in a pack.
Let A be the event of drawing a king.
$\therefore n\left(A\right)=4$
Therefore probability of drawing a king from 48 remaining cards is
$P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}$
$P\left(A\right)=\frac{4}{48}=\frac{1}{12}$
(2) of red colour
After removing 2 red queens, there remain 24 red colour cards in a pack.
Let B be the event of drawing a red colour card from remaining 48 cards.
$\therefore n\left(B\right)=24$
Therefore probability of drawing a red colour card is
$P\left(B\right)=\frac{n\left(B\right)}{n\left(S\right)}$
$P\left(B\right)=\frac{24}{48}=\frac{1}{2}$
(3) a face card
2 red queen and 2 black jacks are removed from a pack. Therefore, total face cards remaining are 8.
Let C be the event of drawing a face card.
$\therefore n\left(C\right)=8$
Therefore probability of drawing a face card is
$P\left(C\right)=\frac{n\left(C\right)}{n\left(S\right)}$
$P\left(C\right)=\frac{8}{48}=\frac{1}{6}$
(4) a queen
There are remaining only 2 queens after removing 2 red queens.
Let D be the event of drawing a queen.
$\therefore n\left(D\right)=2$
Therefore probability of drawing a queen is
$P\left(D\right)=\frac{n\left(D\right)}{n\left(S\right)}$
$P\left(D\right)=\frac{2}{48}=\frac{1}{24}$