What is the probability that card drawn at random from a pack of cards is either red or a king?
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(i) A black king Show Total number of cards are 52 Number of black king cards = 2 Probability of getting black king cards is = Total number of black king cards/Total number of cards = 2/52 = 1/26 ∴ Probability of getting black king cards is 1/26 (ii) Either a black card or a king Total number of cards are 52 Number of either a black card or a king = 28 Probability of getting either a black card or a king is = Total number of either black or king card/Total number of cards = 28/52 = 7/13 ∴ Probability of getting either a black card or a king is 7/13 (iii) Black and a king Total number of cards are 52 Number of black and a king = 2 Probability of getting black and a king is = Total number of black and king card/Total number of cards = 2/52 = 1/26 ∴ Probability of getting black and a king is 1/26 (iv) a jack, queen or a king Total number of cards are 52 Number of a jack, queen or a king = 12 Probability of getting a jack, queen or a king is = Total number of jack, queen or king card/Total number of cards = 12/52 = 3/13 ∴ Probability of getting a jack, queen or a king is 3/13 (v) Neither a heart nor a king Total numbers of cards are 52 Total number of heart cards = 13 Probability of getting a heart is = Total number of hearts/Total number of cards = 13/52 = 1/4 Total number of king cards = 4 Probability of getting a king is = Total number of king card/Total number of cards = 4/52 = 1/13 Total probability of getting a heart and a king = 13/52 + 4/52 – 1/52 = (13+4-1)/52 = 16/52 = 4/13 ∴ Probability of getting neither a heart nor a king = 1 – 4/13 = (13-4)/13 = 9/13 (vi) Spade or an ace Total numbers of cards are 52 Number of spade cards = 13 Probability of getting spade cards is = Total number of spade card/Total number of cards = 13/52 Number of ace cards = 4 Probability of getting ace cards is = Total number of ace card/Total number of cards = 4/52 = 1/13 Probability of getting ace and spade cards is = Total number of ace and spade card/Total number of cards = 1/52 Probability of getting an ace or spade cards is = 13/52 + 4/52 – 1/52 = (13+4-1)/52 = 16/52 = 4/13 ∴ Probability of getting an ace or spade cards is = 4/13 (vii) Neither an ace nor a king Total numbers of cards are 52 Number of king cards = 4 Number of ace cards = 4 Total number of cards = 4 + 4 = 8 Total number of neither an ace nor a king are = 52 – 8 = 44 Probability of getting neither an ace nor a king is = Total number of neither ace nor king card/Total number of cards = 44/52 = 11/13 ∴ Probability of getting neither an ace nor a king is 11/13 (viii) Neither a red card nor a queen Total numbers of cards are 52 Red cards include hearts and diamonds Number of hearts in a deck of 52 cards = 13 Number of diamonds in a deck of 52 cards = 13 Number of queen in a deck of 52 cards = 4 Total number of red card and queen = 13 + 13 + 2 = 28 [since queen of heart and queen of diamond are removed] Number of card which is neither a red card nor a queen = 52 - 28 = 24 Probability of getting neither a king nor a queen is = Total number of neither red nor queen card/Total number of cards = 24/52 = 6/13 ∴ Probability of getting neither a king nor a queen is 6/13 (ix) Other than an ace Total numbers of cards are 52 Total number of ace cards = 4 Total number of non-ace cards = 52-4 = 48 Probability of getting non-ace is = Total number of non-ace cards/Total number of cards = 48/52 = 12/13 ∴ Probability of getting non-ace card is 12/13 (x) A ten Total numbers of cards are 52 Total number of ten cards = 4 Probability of getting ten cards is = Total number of ten cards/Total number of cards = 4/52 = 1/13 ∴ Probability of getting ten card is 1/13 (xi) A spade Total numbers of cards are 52 Total number of spade cards = 13 Probability of getting spade is = Total number of spade cards/Total number of cards = 13/52 = 1/4 ∴ Probability of getting a spade is 1/4 (xii) A black card Total numbers of cards are 52 Cards of spades and clubs are black cards. Number of spades = 13 Number of clubs = 13 Total number of black card out of 52 cards = 13 + 13 = 26 Probability of getting black cards is = Total number of black cards/Total number of cards = 26/52 = 1/2 ∴ Probability of getting a black card is 1/2 (xiii) The seven of clubs Total numbers of cards are 52 Total number of the seven of clubs cards = 1 Probability of getting the seven of clubs cards is = Total number of the seven of club cards/ Total numbers of cards = 1/52 ∴ Probability of the seven of club card is 1/52 (xiv) Jack Total numbers of cards are 52 Total number of jack cards = 4 Probability of getting jack cards is = Total number of jack cards/ Total numbers of cards = 4/52 = 1/13 ∴ Probability of the jack card is 1/13 (xv) The ace of spades Total numbers of cards are 52 Total number of the ace of spades cards = 1 Probability of getting ace of spade cards is = Total number of ace of spade cards/ Total numbers of cards = 1/52 ∴ Probability of the ace of spade card is 1/52 (xvi) A queen Total numbers of cards are 52 Total number of queen cards = 4 Probability of getting queen cards is = Total number of queen cards/Total numbers of cards = 4/52 = 1/13 ∴ Probability of a queen card is 1/13 (xvii) A heart Total numbers of cards are 52 Total number of heart cards = 13 Probability of getting queen cards is = Total number of heart cards/Total numbers of cards = 13/52 = 1/4 ∴ Probability of a heart card is 1/4 (xviii) A red card Total numbers of cards are 52 Total number of red cards = 13+13 = 26 Probability of getting queen cards is = Total number of red cards/Total numbers of cards = 26/52 = 1/2 ∴ Probability of a red card is 1/2 What is the probability that the card is either a red card or a king?`therefore n(E_(2)) = (26 + 2) = 28` `therefore` P(getting a red card or a king) `= P(E_(2)) = (n(E_(2)))/(n(S)) = 28/52 = 7/13. What is the probability of getting a red and a king?Hence, the probability of getting a king of red colour is 1/26. Was this answer helpful?
What is the probability that the randomly drawn card will be a red card?So, the probability of drawing a red-faced card is 6 out of 52 cards. Thus, the probability of drawing a red face card from a deck of cards is 6/52 = 3/26.
What is the probability of getting a red card or a king in a well shuffled pack of 52 cards?` P(getting a red king) ` = 2/52 = 1/26`.
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