one card is drawn randomly,from a well-shuffled pack of 52 cards. then find the probability that the card drawn is
a. a queen b. a king c. a jack d. an ace e. 8 of diamonds f. a face card g. a black face card h. a red face card i. a black card j. red and jack k. either red or jack l. 8 of black suit m. 7 of red suits
Answers
In a playing card there are 52 cards.
Therefore the total number of possible outcomes = 52
(i) ‘2’ of spades:
Number of favorable outcomes i.e. ‘2’ of spades is 1 out of 52 cards.
Therefore, probability of getting ‘2’ of spade
Number of favorable outcomesP(A) = Total number of possible outcome
= 1/52
(ii) a jack
Number of favorable outcomes i.e. ‘a jack’ is 4 out of 52 cards.
Therefore, probability of getting ‘a jack’
Number of favorable outcomesP(B) = Total number of possible outcome
= 4/52
= 1/13
(iii) a king of red color
Number of favorable outcomes i.e. ‘a king of red color’ is 2 out of 52 cards.
Therefore, probability of getting ‘a king of red color’
Number of favorable outcomesP(C) = Total number of possible outcome
= 2/52
= 1/26
(iv) a card of diamond
Number of favorable outcomes that is ‘a card of diamond’ is 13 out of 52 cards.
Therefore, probability of getting ‘a card of diamond’
Number of favorable outcomesP(D) = Total number of possible outcome
= 13/52
= 1/4
(v) a king or a queen
Total number of king is 4 out of 52 cards.
Total number of queen is 4 out of 52 cards
Number of favorable outcomes i.e. ‘a king or a queen’ is 4 + 4 = 8 out of 52 cards.
Therefore, probability of getting ‘a king or a queen’
Number of favorable outcomesP(E) = Total number of possible outcome
= 8/52
= 2/13
(vi) a non-face card
Total number of face card out of 52 cards = 3 times 4 = 12
Total number of non-face card out of 52 cards = 52 - 12 = 40
Therefore, probability of getting ‘a non-face card’
Number of favorable outcomesP(F) = Total number of possible outcome
= 40/52
= 10/13
(vii) a black face card:
Cards of Spades and Clubs are black cards.
Number of face card in spades (king, queen and jack or knaves) = 3
Number of face card in clubs (king, queen and jack or knaves) = 3
Therefore, total number of black face card out of 52 cards = 3 + 3 = 6
Therefore, probability of getting ‘a black face card’
Number of favorable outcomesP(G) = Total number of possible outcome
= 6/52
= 3/26
(viii) a black card:
Cards of spades and clubs are black cards.
Number of spades = 13
Number of clubs = 13
Therefore, total number of black card out of 52 cards = 13 + 13 = 26
Therefore, probability of getting ‘a black card’
Number of favorable outcomesP(H) = Total number of possible outcome
= 26/52
= 1/2
(ix) a non-ace:
Number of ace cards in each of four suits namely spades, hearts, diamonds and clubs = 1
Therefore, total number of ace cards out of 52 cards = 4
Thus, total number of non-ace cards out of 52 cards = 52 - 4
= 48
Therefore, probability of getting ‘a non-ace’
Number of favorable outcomesP(I) = Total number of possible outcome
= 48/52
= 12/13
(x) non-face card of black colour:
Cards of spades and clubs are black cards.
Number of spades = 13
Number of clubs = 13
Therefore, total number of black card out of 52 cards = 13 + 13 = 26
Number of face cards in each suits namely spades and clubs = 3 + 3 = 6
Therefore, total number of non-face card of black colour out of 52 cards = 26 - 6 = 20
Therefore, probability of getting ‘non-face card of black colour’
Number of favorable outcomesP(J) = Total number of possible outcome
= 20/52
= 5/13
(xi) neither a spade nor a jack
Number of spades = 13
Total number of non-spades out of 52 cards = 52 - 13 = 39
Number of jack out of 52 cards = 4
Number of jack in each of three suits namely hearts, diamonds and clubs = 3
[Since, 1 jack is already included in the 13 spades so, here we will take number of jacks is 3]
Neither a spade nor a jack = 39 - 3 = 36
Therefore, probability of getting ‘neither a spade nor a jack’
Number of favorable outcomesP(K) = Total number of possible outcome
= 36/52
= 9/13
(xii) neither a heart nor a red king
Number of hearts = 13
Total number of non-hearts out of 52 cards = 52 - 13 = 39
Therefore, spades, clubs and diamonds are the 39 cards.
Cards of hearts and diamonds are red cards.
Number of red kings in red cards = 2
Therefore, neither a heart nor a red king = 39 - 1 = 38
[Since, 1 red king is already included in the 13 hearts so, here we will take number of red kings is 1]
Therefore, probability of getting ‘neither a heart nor a red king’
Number of favorable outcomesP(L) = Total number of possible outcome
= 38/52
= 19/26
These are the basic problems on probability with playing cards.
HOPE THIS HELPS U...............................^_^
1)a queen = 4/52
= 1/13
2)a king = 4/52
1/13
3)a jack = 4/52
1/13
4)an ace = 4/52
1/13
5) 8 of diamond = 1/52
6)a face card = 12/52
3/13
7) black face card = 6/52
3/26
8) a red face card = 6/52
3/26
9) a black card = 26/52
3/4
10) red jack = 2/52
1/26
11) red jack = 2/52
1/26
12) black suit = 2/52
1/ 26
13) red suit = 2/52
1/ 26