Question

$\left(A\right)$ From a pack of $52$ playing cards jacks, queens, kings and aces of red colour are removed. From the remaining, a card is drawn at random. Find the probability that the card drawn is
$\left(i\right)$ a black queen
$\left(ii\right)$ a red card
$\left(iii\right)$ a ten
$\left(iv\right)$ a picture card [jacks, queens and kings are picture cards]
$\left(B\right)$ All cards of ace, jack and queen are removed from a deck of playing cards. One card is drawn at random from the remaining cards. Find the probability that the card drawn is
$\left(i\right)$ A face card
$\left(ii\right)$ Not a face card.

• A. $\left(A\right)\left(i\right)\frac{1}{22},\left(ii\right)\frac{9}{22},\left(iii\right)\frac{1}{11},\left(iv\right)\frac{3}{22}\left(B\right)\left(i\right)\frac{1}{10},\left(ii\right)\frac{9}{10}$
• B. $\left(A\right)\left(i\right)\frac{1}{14},\left(ii\right)\frac{5}{22},\left(iii\right)\frac{1}{11},\left(iv\right)\frac{6}{13}\left(B\right)\left(i\right)\frac{1}{10},\left(ii\right)\frac{9}{10}$
• C. $\left(A\right)\left(i\right)\frac{1}{17},\left(ii\right)\frac{9}{22},\left(iii\right)\frac{1}{11},\left(iv\right)\frac{11}{13}\left(B\right)\left(i\right)\frac{1}{10},\left(ii\right)\frac{9}{10}$
• D. None of these

Answer 1

The correct option is A $\left(A\right)\left(i\right)\frac{1}{22},\left(ii\right)\frac{9}{22},\left(iii\right)\frac{1}{11},\left(iv\right)\frac{3}{22}\left(B\right)\left(i\right)\frac{1}{10},\left(ii\right)\frac{9}{10}$

(a) Total cards = $52-8=44$
(i) No. of queens of black colour = $2$
$\therefore$ probability = $\frac{2}{44}=\frac{1}{22}$
(ii) No. of red cards =$26-8=18$
$\therefore$ probability = $\frac{18}{44}=\frac{9}{22}$
(iii) no. of tens = $4$
$\therefore$ probability = $\frac{4}{44}=\frac{1}{11}$
(iv) No. of remaining picture cards =$2+2+2=6$
$\therefore$ probability = $\frac{6}{44}=\frac{3}{22}$
(b) Total cards = $52-12=40$
(i) No. of remaining face cards (only Kings are remaining) = $4$
$\therefore$ probability = $\frac{4}{40}=\frac{1}{10}$
(ii) No. of cards that are not face cards = $36$
$\therefore$ probability = $\frac{36}{40}=\frac{9}{10}$