Question

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
(i) a black queen (ii) a red card (iii) a ten
(iv) a picture card (jacks, queen and kings are picture cards).

Answer 1

Number of cards removed = ` 2+2+2+2=8`.
Total number of remaining cards = 52 - 8 = 44.
Now, there are 2 jacks, 2 queens, 2 kings and 2 aces of black colour only.
(i) Number of black queens = 2.
`:. ` P(getting a black queen) ` = 2/44 = 1/22`.
(ii) Remaining number of red cards = 26 - 8 = 18.
`:. ` P(getting a red card) = `18/44 = 9/22`.
(iii) Number of tens = 4.
` :. ` P(getting a tan) ` = 4/44 = 1/11`.
(iv) We kown that jacks, queen and kings are picture cards.
Out of 12 picture cards, it is given that 6 have been
removed. So, the remaining number of picture cards = 12 - 6 = 6.
` :. ` P(getting a picture card) ` = 6/44 = 3/22`.