Question

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting
$\left(a\right)\left(i\right)$ a king of red colour $\left(ii\right)$ A face card
$\left(iii\right)$ A red face card $\left(iv\right)$ A jack of hearts
$\left(b\right)\left(i\right)$ A spade
$\left(ii\right)$ the queen of diamonds
$\left(iii\right)$ Neither a red card nor a queen
$\left(c\right)\left(i\right)$ A non-face card
$\left(ii\right)$ a black king or a red queen

• A. $\left(a\right)\left(i\right)\frac{1}{26}\left(ii\right)\frac{3}{13}\left(iii\right)\frac{3}{26}\left(iv\right)\frac{1}{52}$
• B. $\left(b\right)\left(i\right)\frac{1}{4}\left(ii\right)\frac{1}{52}\left(iii\right)\frac{6}{13}$
• C. $\left(c\right)\left(i\right)\frac{10}{13}\left(ii\right)\frac{1}{13}$
• D. None of the above

Answer 1

Answer: (A), (B), (C)

$\left(a\right)\left(i\right)\frac{1}{26}\left(ii\right)\frac{3}{13}\left(iii\right)\frac{3}{26}\left(iv\right)\frac{1}{52}$
$\left(b\right)\left(i\right)\frac{1}{4}\left(ii\right)\frac{1}{52}\left(iii\right)\frac{6}{13}$
$\left(c\right)\left(i\right)\frac{10}{13}\left(ii\right)\frac{1}{13}$

In 52 cards getting a one card as 52 times
a.(1) The king in card is two getting in 2 times
Then probability =$\frac{2}{52}=\frac{1}{26}$
(ii)In 52 cards the king ,queen and joker are three face card.Then total face cards are 12.So these card get 12 times
Then probability =$\frac{12}{52}=\frac{3}{13}$
(!!!)In 52 cards the red face card are 3 face card.Then total
red face cards are 3.So these card get 6 times
Then probability =$\frac{6}{52}=\frac{3}{26}$
(iv)In 52 cards the jack of heart card is one .So the getting time card is one
Then probability =$\frac{1}{52}
(b) (i)In 52 cards the spade cards are 13. So getting time is 13
Then probability =$\frac{13}{52}=\frac{1}{4}$
(ii)In 52 cards the queen of diamonds is one .So getting time is one
Then probevility=$\frac{1}{52}$
(iii)In 52 cards Neither a red card nor a queen the total cards are
24.So time of getting cards are 24
Then probability =$\frac{24}{52}=\frac{6}{13}$
(c) (i)In 52 cards non-face cards are 40.So timie of getting cards are 40.
Then probability =$\frac{24}{52}=\frac{6}{13}$
(ii)In 52 cards a black king or a red queen are 4.So getting time is 4.
Then probability =$\frac{4}{52}=\frac{1}{13}$