Question

All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is: (i) a red card (ii) a face card and (iii) a card of clubs.

Answer 1

i) There are 12 face cards in all in pack of 52 cards.

Out of that there are 6 red face cards. (52 - 6 = 46)

Out of 12 face cards, 6 red face cards are removed.

Hence, remaining red cards = 26 - 6= 20

The probability of getting the red from remaining 46 cards = $\frac{20}{46}$ = $\frac{10}{23}$

ii) There are 2 black jacks, 2 black queens and 2 black kings i.e. total 6 face cards in 46 cards.

The probability of getting a face card $\frac{6}{46}$ = $\frac{3}{23}$

(iii) There are 13 cards of clubs

Probability= $\frac{13}{46}$