Question

All the black face cards are removed from a pack of 52 playing cards.
The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a (i) face card, (ii) red card, (iii) black card, (iv) king.

Answer 1

Out of 52 playing cards, 2 black jacks, 2 black queen and 2 black kings have been removed.
Total number of remaining cards = (52-6) = 46.
(i) Now, there are 6 face cards in the remaining cards.
`:. ` P(getting a face card) = ` 6/46 = 3/23`.
(ii) There are 26 red cards.
` :. ` P(getting a red card) ` = 26/46 = 13/23`.
(iii) Out of 46 cards, number of black cards = 26 -6 = 20.
` :. ` P( getting a black card) ` = 20/46 = 10/23`.
(iv) Now, these 46 cards have 2 kings.
` :. ` P(getting a king) =` 2/46 = 1/23`.