# 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

Grade:12th pass

## 1 Answers

Pawan Prajapati
askIITians Faculty 60785 Points
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.