A card is drawn from a well shuffled pack of 52 cards. Find the probability that the card drawn is :
(i) a red face card
(ii) neither a club nor a spade
(iii) neither an ace nor a king of red colour
(iv) neither a red card nor a queen
(v) neither a red card nor a black king.

Question

A card is drawn from a well shuffled pack of 52 cards. Find the probability that the card drawn is :
(i) a red face card
(ii) neither a club nor a spade
(iii) neither an ace nor a king of red colour
(iv) neither a red card nor a queen
(v) neither a red card nor a black king.

KnowledgeBoat · Accepted Answer

Well shuffling ensures equally likely outcomes. Total number of outcomes = 52. (i) Each suit has one king, one queen and one jack, and there are two suits of red colour. ∴ There are 2 kings, 2 queens and 2 jacks. ∴ The number of red face cards = 6. ∴ P(a red face card) = Hence, the probability that a card drawn is a red face card = . (ii) There are 13 clubs and 13 spades i.e. total = 26 cards. No. of cards left other than spades and clubs = 52 - 26 = 26. P(neither a club nor spade) = Hence, the probability that a card drawn is neither a club nor spade card = . (iii) There are 2 kings of red colour, one of heart and one of diamond. There are 4 aces, one of each suit. No. of cards other than ace and king of red colour = 52 - 4 - 2 = 46. P(neither an ace nor a king of red colour) = Hence, the probability that a card drawn is neither an ace nor a king of red colour = . (iv) There are 26 red cards, 13 of hearts and 13 of diamonds. There are 4 queens, one of each suit but since red queens are included in red cards hence, queens left = 2. Total no. of red cards and queen = 26 + 2 = 28. No. of cards other than queen and red cards = 52 - 28 = 24. P(neither a red card nor queen) = Hence, the probability that a card drawn is neither a red card nor queen = (v) There are 26 red cards, 13 of hearts and 13 of diamonds. There are 2 black kings, one of club and one of spade. Total no. of red cards and black kings = 26 + 2 = 28. No. of cards other than red cards and black kings = 52 - 28 = 24. P(neither a red card nor black king) = Hence, the probability that a card drawn is neither a red card nor black king =

Mathematics

A card is drawn from a well shuffled pack of 52 cards. Find the probability that the card drawn is :
(i) a red face card
(ii) neither a club nor a spade
(iii) neither an ace nor a king of red colour
(iv) neither a red card nor a queen
(v) neither a red card nor a black king.

Probability

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Mathematics

A card is drawn from a well shuffled pack of 52 cards. Find the probability that the card drawn is :(i) a red face card(ii) neither a club nor a spade(iii) neither an ace nor a king of red colour(iv) neither a red card nor a queen(v) neither a red card nor a black king.

Probability

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(v) neither a red card nor a black king.

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