A card is drawn from a well-shuffled pack of 52 cards.

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A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting:
(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
Number of possible outcome = 52
(i) Probability of‘2’ of spade will be
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 1 }{ 52 }
(ii) There are 4 jack card Probability of jack will be
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 4 }{ 52 }
= \\ \frac { 1 }{ 13 }
(iii) King of red colour are 2 in number
Probability of red colour king will be
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 2 }{ 52 }
= \\ \frac { 1 }{ 26 }
(iv) Cards of diamonds are 13 in number
Probability of diamonds card will be
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 13 }{ 52 }
= \\ \frac { 1 }{ 4 }
(v) Number of kings and queens = 4 + 4 = 8
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 8 }{ 52 }
= \\ \frac { 2 }{ 13 }
(vi) Non-face cards are = 52 – 3 × 4 = 52 – 12 = 40
Probability of non-face card will be
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 40 }{ 52 }
= \\ \frac { 10 }{ 13 }
(vii) Black face cards are = 2 × 3 = 6
Probability of black face card will be
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 6 }{ 52 }
= \\ \frac { 3 }{ 26 }
(viii) No. of black cards = 13 x 2 = 26
Probability of black card will be
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 26 }{ 52 }
= \\ \frac { 1 }{ 2 }
(ix) Non-ace cards are 12 × 4 = 48
Probability of non-ace card will be
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 48 }{ 52 }
= \\ \frac { 12 }{ 13 }
(x) Non-face card of black colours are 10 × 2 = 20
Probability of non-face card of black colour will be
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 20 }{ 52 }
= \\ \frac { 5 }{ 13 }
(xi) Number of card which are neither a spade nor a jack
= 13 × 3 – 3 = 39 – 3 = 36
Probability of card which is neither a spade nor a jack will be
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 36 }{ 52 }
= \\ \frac { 9 }{ 13 }
(xii) Number of cards which are neither a heart nor a red king
= 3 × 13 = 39 – 1 = 38
Probability of card which is neither a heart nor a red king will be
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 38 }{ 52 }
= \\ \frac { 19 }{ 26 }

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