The king,queen,and jack of clubs are removed from a deck of $52$ playing cards and then well shuffled. Now,one card is drawn at random from the remaining cards. What is the probability that the card is:
$(i)$ a club
$(ii)$ $10$ of hearts
$(i)$ a club
$(ii)$ $10$ of hearts
(A) $(i)$ Let $E_1$ be the event of getting a club.
Total cards remaining $= 52 - 3 = 49$.
Number of clubs remaining $= 13 - 3 = 10$.
$\therefore$ Probability $= \frac{10}{49}$.
$(ii)$ Let $E_2$ be the event of getting $10$ of hearts.
There is only one $10$ of hearts in the deck.
$\therefore$ Probability $= \frac{1}{49}$.
Total cards remaining $= 52 - 3 = 49$.
Number of clubs remaining $= 13 - 3 = 10$.
$\therefore$ Probability $= \frac{10}{49}$.
$(ii)$ Let $E_2$ be the event of getting $10$ of hearts.
There is only one $10$ of hearts in the deck.
$\therefore$ Probability $= \frac{1}{49}$.
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