# All the black face cards are removed from a pack of 52 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

Pawan Prajapati
one year ago
In a deck of cards there are 26 black cards and 26 red cards, out of which there are 12 face cards-6 black and 6 red. So before starting the solution remove 6 black face cards from the deck of cards and use the formula Probability=favorable outcometotal no of outcome. Complete step-by-step answer: We know that there are 6 black face cards in a deck of cards , 2 king of black , 2 queen of black and 2 jack of black. Remaining card in the bundle after removing 6 black face cards is ⇒52 - 6 = 46 (i) Favorable outcome of a face card = we know there are 6 red face cards , 2 red king , 2 red queen and 2 red jack. p(red face card) = favorable outcometotal no of outcome=646=323 (ii) Favorable outcome of red card = we know that there are 26 red cards , and all the red cards in the deck. p(red card) = favorable outcometotal no of outcome=2646=1323 (iii) Favorable outcome of black card = we know that there are 26 black cards in which 6 black face cards are removed. ∴ Remaining black cards = 26 - 6 = 20. p(black card) = favorable outcometotal no of outcome=2046=1023 (iv) Favorable outcome of a king = there are 4 kings in a deck of a card in which we remove 2 cards. ∴ Remaining kings = 4 - 2 = 2 p(king)=favorable outcometotal no of outcome=246=123 Note: - For solving the question of probability , first we have to find a favorable outcome and then divide it by total no of outcomes to get the probability.
Debarati
105 Points
one year ago
After removing all the black face cards, 46 cards are remaing.
(i) No. of face cards= 6 (6 have been removed)
Probability of getting a face card= 6/46= 3/23
(ii) No. of red cards= 26
Probability of getting a red card= 26/46= 13/23
(iii) No. of black cards= 20 (6 have been removed)
Probability of getting a black card= 20/46= 10/23
(iv) No. of king cards= 2 (2 have been removed)
Probability of getting a king card= 2/46= 1/23

I hope you have understood.