PROBLEMS
1. A card is drawn from a well shuffled pack of 52
cards. Find the probability of:
(i) ‘2’ of spades
(ii) a jack
(iii) a king of red colour
(iv) a card of diamond
(v) a king or a queen
(vi) a non-face card
(vii) a black face card
(viii) a black card
(ix) a non-ace
(x) non-face card of black colour
(xi) neither a spade nor a jack
(xii) neither a heart nor a red king
SOLUTION:
In a playing card there are 52 cards.
Therefore the total number of possible outcomes
n(s)= 52
(I) ‘2’ OF SPADES:
Number of favourable outcomes i.e. ‘2’ of spades
is 1 out of 52 cards.
Therefore, probability of getting ‘2’ of spade
We know:
P(A) = 1/52
(II) A JACK Therefore, probability of getting ‘a king or a
queen’
Number of favourable outcomes i.e. ‘a jack’ is 4
out of 52 cards. We know:
Therefore, probability of getting ‘a jack’
P(B) = 8/52
We know:
P(B) = 2/13
(VI) A NON-FACE CARD
P(B) = 4/52
P(B) = 1/13 Total number of face card out of 52 cards = 3
times 4 = 12
(III) A KING OF RED COLOUR
Total number of non-face card out of 52 cards =
Number of favourable outcomes i.e. ‘a king of red 52 - 12 = 40
colour’ is 2 out of 52 cards.
Therefore, probability of getting ‘a non-face card’
Therefore, probability of getting ‘a king of red
colour’ We know:
We know:
P(B) = 40/52
= 10/13
P(B) = 2/52
P(B) = 1/26
(IV) A CARD OF DIAMOND (VII) A BLACK FACE CARD:
Number of favourable outcomes i.e. ‘a card of Cards of Spades and Clubs are black cards.
diamond’ is 13 out of 52 cards.
Number of face card in spades (king, queen and
Therefore, probability of getting ‘a card of jack or knaves) = 3
diamond’
Number of face card in clubs (king, queen and
We know: 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
P(D) = 13/52
card’
P(D) = 1/4
We know:
(V) A KING OR A QUEEN
Total number of king is 4 out of 52 cards. P(A) = 6/52
P(A) = 3/26
Total number of queen is 4 out of 52 cards
Number of favourable outcomes i.e. ‘a king or a
queen’ is 4 + 4 = 8 out of 52 cards.
(VIII) A BLACK CARD: Number of face cards in each suits namely spades
and clubs = 3 + 3 = 6
Cards of spades and clubs are black cards.
Therefore, total number of non-face card of black
Number of spades = 13 colour out of 52 cards = 26 - 6 = 20
Number of clubs = 13 Therefore, probability of getting ‘non-face card of
black colour’
Therefore, total number of black card out of 52
cards = 13 + 13 = 26 We know:
Therefore, probability of getting ‘a black card’
We know:
P(A) = 20/52
= 5/13
P(A) = 26/52
P(A) = 1/2 (XI) NEITHER A SPADE NOR A JACK
Number of spades = 13
(IX) A NON-ACE: Total number of non-spades out of 52 cards = 52 -
13 = 39
Number of ace cards in each of four suits namely
spades, hearts, diamonds and clubs = 1 Number of jack out of 52 cards = 4
Therefore, total number of ace cards out of 52 Number of jack in each of three suits
cards = 4 namely hearts, diamonds and clubs = 3
Thus, total number of non-ace cards out of 52 [Since, 1 jack is already included in the 13 spades
cards = 52 - 4 so, here we will take number of jacks is 3]
= 48 Neither a spade nor a jack = 39 - 3 = 36
Therefore, probability of getting ‘a non-ace’ Therefore, probability of getting ‘neither a spade
nor a jack’
We Know:
We know:
P(A) = 48/52
= 12/13 P(A) = 36/52
= 9/13
(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
(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’
We know:
P(B) = 38/52
= 19/26
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