a card is drown from a well shuffled deck of 52 cards find the probability that it is
(a) an jake
(b) an ace of spade
(c) a queen
(d) a heart
(e) a red card
(f) a card of club
(g) a ‘9’ of heart
(h) a black king
(I) a non face card
(j) a black king or red queen
Step-by-step explanation:
(a) an jake
There are 4 jake(s) in a deck of cards.
So, 4/52 = 1/13 is the answer.
(b) an ace of spade
There is only one, so
1/52 is the answer.
(c) a queen
There are 4 queens.
So, 4/52 = 1/13 is the answer.
(d) a heart
There are 13 hearts in a deck of cards.
13/52 = 1/4 is the answer.
(e) a red card
There are 2 pairs- A heart and a diamond.
So, they are 13 each in total.
13×2 = 26
So, 26/52 = 1/2 is the required answer.
(f) a card of club
There are 13 cards of clubs.
So, 13/52 = 1/4 is the required answer.
(g) a ‘9’ of heart
There is one and only 9 of heart.
So, 1/52 is the answer.
(h) a black king
There are Spades and Clubs in black, having 1 king each.
So, 1×2 = 2 kings in total
So, 2/52 = 1/26 is the required answer.
(I) a non face card
There are 10 non face cards (3 in jake, king and queen)
So, there are 4 categories:- Spade, Heart, Club, Diamond.
So, 4×10 = 40 cards.
So, 40/52 = 10/26 = 5/13 is the required answer.
(j) a black king or red queen
There are 2 black categories :- Spade and Club, so, 2 kings. There are 2 red categories – Heart and Diamond, having 2 queens (1 in each).
So, 2+2=4
4/56 = 1/13 is the required answer [tex].[/tex]
Answer:
Given :-
[tex]\mapsto[/tex] A card is drawn from a well shuffled deck of 52 cards.
To Find :-
[tex]\mapsto[/tex] What is the probability of :
Formula Used :-
[tex]\clubsuit[/tex] Probability Formula :
[tex]\longmapsto \sf\boxed{\bold{\pink{Probability (P) =\: \dfrac{Number\: of\: favorable\: outcomes}{Total\: number\: of\: possible\: outcomes}}}}\\[/tex]
Solution :-
[tex]\mapsto[/tex] A card is drawn from a well shuffled deck of 52 cards :
➲ (a) An jake :
As we know that :
[tex]\bigstar[/tex] 4 jacks contain in a deck of cards.
Given :
According to the question by using the formula we get,
[tex]\implies \sf Probability (P) =\: \dfrac{\cancel{4}}{\cancel{52}}[/tex]
[tex]\implies\sf Probability (P) =\: \dfrac{\cancel{2}}{\cancel{26}}[/tex]
[tex]\implies \sf\bold{\red{Probability (P) =\: \dfrac{1}{13}}}[/tex]
[tex]\rule{150}{2}[/tex]
➲ (b) An ace of spade :
As we know that :
[tex]\bigstar[/tex] 1 ace of spade contain in a deck of cards.
Given :
According to the question by using the formula we get,
[tex]\implies \sf Probability (P) =\: \dfrac{1}{52}[/tex]
[tex]\implies \sf\bold{\red{Probability (P) =\: \dfrac{1}{52}}}[/tex]
[tex]\rule{150}{2}[/tex]
➲ (c) A queen :
As we know that :
[tex]\bigstar[/tex] 4 queen contain in a deck of cards.
Given :
According to the question by using the formula we get,
[tex]\implies\sf Probability (P) =\: \dfrac{\cancel{4}}{\cancel{52}}[/tex]
[tex]\implies \sf Probability (P) =\: \dfrac{\cancel{2}}{\cancel{26}}[/tex]
[tex]\implies \sf\bold{\red{Probability (P) =\: \dfrac{1}{13}}}[/tex]
[tex]\rule{150}{2}[/tex]
➲ (d) A heart :
As we know that :
[tex]\bigstar[/tex] 13 heart contain in a deck of cards.
Given :
According to the question by using the formula we get,
[tex]\implies \sf Probability (P) =\: \dfrac{\cancel{13}}{\cancel{52}}[/tex]
[tex]\implies \sf\bold{\red{Probability (P) =\: \dfrac{1}{4}}}[/tex]
[tex]\rule{150}{2}[/tex]
➲ (e) A red heart :
As we know that :
[tex]\bigstar[/tex] There are 26 red heart.
[tex]\leadsto[/tex] Heart = 13
[tex]\leadsto[/tex] Diamond = 13
Given :
According to the question by using the formula we get,
[tex]\implies \sf Probability (P) =\: \dfrac{\cancel{26}}{\cancel{52}}[/tex]
[tex]\implies \sf Probability (P) =\: \dfrac{\cancel{13}}{\cancel{26}}[/tex]
[tex]\implies \sf\bold{\red{Probability (P) =\: \dfrac{1}{2}}}[/tex]
[tex]\rule{150}{2}[/tex]
➲ (f) A card of club :
As we know that :
[tex]\bigstar[/tex] 13 card of club contain in a deck of cards.
Given :
According to the question by using the formula we get,
[tex]\implies \sf Probability (P) =\: \dfrac{\cancel{13}}{\cancel{52}}[/tex]
[tex]\implies \sf\bold{\red{Probability (P) =\: \dfrac{1}{4}}}[/tex]
[tex]\rule{150}{2}[/tex]
➲ (g) A ‘9‘ of heart :
As we know that :
[tex]\bigstar[/tex] 1 heart contain in a deck of cards.
Given :
According to the question by using the formula we get,
[tex]\implies \sf\bold{\red{Probability (P) =\: \dfrac{1}{52}}}[/tex]
[tex]\rule{150}{2}[/tex]
➲ (h) A black king :
As we know that :
[tex]\bigstar[/tex] 2 black king contain in a deck of cards.
Given :
According to the question by using the formula we get,
[tex]\implies \sf Probability (P) =\: \dfrac{\cancel{2}}{\cancel{52}}[/tex]
[tex]\implies \sf\bold{\red{Probability (P) =\: \dfrac{1}{26}}}[/tex]
[tex]\rule{150}{2}[/tex]
➲ (i) A non face card :
As we know that :
[tex]\bigstar[/tex] 40 non face card contain in a deck of cards.
Given :
According to the question by using the formula we get,
[tex]\implies \sf Probability (P) =\: \dfrac{\cancel{40}}{\cancel{52}}[/tex]
[tex]\implies \sf Probability (P) =\: \dfrac{\cancel{20}}{\cancel{26}}[/tex]
[tex]\implies\sf\bold{\red{Probability (P) =\: \dfrac{10}{13}}}[/tex]
[tex]\rule{150}{2}[/tex]
➲ (j) A black king or red queen :
[tex]\mapsto[/tex] Black king = 2
[tex]\mapsto[/tex] Red Queen = 2
Then,
[tex]\bigstar[/tex] 4 card of a black king and red queen in a deck of cards.
Given :
According to the question by using the formula we get,
[tex]\implies\sf Probability (P) =\: \dfrac{\cancel{4}}{\cancel{52}}[/tex]
[tex]\implies \sf\bold{\red{Probability (P) =\: \dfrac{1}{13}}}[/tex]
[tex]\rule{150}{2}[/tex]