Question

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 ​

Answer 1

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 $.$

Answer 2

Answer:

Given :-

$\mapsto$ A card is drawn from a well shuffled deck of 52 cards.

To Find :-

$\mapsto$ What is the probability of :

• An jake
• An ace of spade
• A queen
• A heart
• A red card
• A card of club
• A '9' of heart
• A black king
• A non face card
• A black king or red queen

Formula Used :-

$\clubsuit$ Probability Formula :

$\longmapsto \sf\boxed{\bold{\pink{Probability (P) =\: \dfrac{Number\: of\: favorable\: outcomes}{Total\: number\: of\: possible\: outcomes}}}}$

Solution :-

$\mapsto$ A card is drawn from a well shuffled deck of 52 cards :

➲ (a) An jake :

As we know that :

$\bigstar$ 4 jacks contain in a deck of cards.

Given :

• Number of favorable outcomes = 4
• Total number of possible outcomes = 52

According to the question by using the formula we get,

$\implies \sf Probability (P) =\: \dfrac{\cancel{4}}{\cancel{52}}$

$\implies\sf Probability (P) =\: \dfrac{\cancel{2}}{\cancel{26}}$

$\implies \sf\bold{\red{Probability (P) =\: \dfrac{1}{13}}}$

$\rule{150}{2}$

➲ (b) An ace of spade :

As we know that :

$\bigstar$ 1 ace of spade contain in a deck of cards.

Given :

• Number of favorable outcomes = 1
• Total number of possible outcomes = 52

According to the question by using the formula we get,

$\implies \sf Probability (P) =\: \dfrac{1}{52}$

$\implies \sf\bold{\red{Probability (P) =\: \dfrac{1}{52}}}$

$\rule{150}{2}$

➲ (c) A queen :

As we know that :

$\bigstar$ 4 queen contain in a deck of cards.

Given :

• Number of favorable outcomes = 4
• Total number of possible outcomes = 52

According to the question by using the formula we get,

$\implies\sf Probability (P) =\: \dfrac{\cancel{4}}{\cancel{52}}$

$\implies \sf Probability (P) =\: \dfrac{\cancel{2}}{\cancel{26}}$

$\implies \sf\bold{\red{Probability (P) =\: \dfrac{1}{13}}}$

$\rule{150}{2}$

➲ (d) A heart :

As we know that :

$\bigstar$ 13 heart contain in a deck of cards.

Given :

• Number of favorable outcomes = 13
• Total number of possible outcomes = 52

According to the question by using the formula we get,

$\implies \sf Probability (P) =\: \dfrac{\cancel{13}}{\cancel{52}}$

$\implies \sf\bold{\red{Probability (P) =\: \dfrac{1}{4}}}$

$\rule{150}{2}$

➲ (e) A red heart :

As we know that :

$\bigstar$ There are 26 red heart.

$\leadsto$ Heart = 13

$\leadsto$ Diamond = 13

Given :

• Number of favorable outcomes = 26
• Total number of possible outcomes = 52

According to the question by using the formula we get,

$\implies \sf Probability (P) =\: \dfrac{\cancel{26}}{\cancel{52}}$

$\implies \sf Probability (P) =\: \dfrac{\cancel{13}}{\cancel{26}}$

$\implies \sf\bold{\red{Probability (P) =\: \dfrac{1}{2}}}$

$\rule{150}{2}$

➲ (f) A card of club :

As we know that :

$\bigstar$ 13 card of club contain in a deck of cards.

Given :

• Number of favorable outcomes = 13
• Total number of possible outcomes = 52

According to the question by using the formula we get,

$\implies \sf Probability (P) =\: \dfrac{\cancel{13}}{\cancel{52}}$

$\implies \sf\bold{\red{Probability (P) =\: \dfrac{1}{4}}}$

$\rule{150}{2}$

➲ (g) A '9' of heart :

As we know that :

$\bigstar$ 1 heart contain in a deck of cards.

Given :

• Number of favorable outcomes = 1
• Total number of possible outcomes = 52

According to the question by using the formula we get,

$\implies \sf\bold{\red{Probability (P) =\: \dfrac{1}{52}}}$

$\rule{150}{2}$

➲ (h) A black king :

As we know that :

$\bigstar$ 2 black king contain in a deck of cards.

Given :

• Number of favorable outcomes = 2
• Total number of possible outcomes = 52

According to the question by using the formula we get,

$\implies \sf Probability (P) =\: \dfrac{\cancel{2}}{\cancel{52}}$

$\implies \sf\bold{\red{Probability (P) =\: \dfrac{1}{26}}}$

$\rule{150}{2}$

➲ (i) A non face card :

As we know that :

$\bigstar$ 40 non face card contain in a deck of cards.

Given :

• Number of favorable outcomes = 10
• Total number of possible outcomes = 52

According to the question by using the formula we get,

$\implies \sf Probability (P) =\: \dfrac{\cancel{40}}{\cancel{52}}$

$\implies \sf Probability (P) =\: \dfrac{\cancel{20}}{\cancel{26}}$

$\implies\sf\bold{\red{Probability (P) =\: \dfrac{10}{13}}}$

$\rule{150}{2}$

➲ (j) A black king or red queen :

$\mapsto$ Black king = 2

$\mapsto$ Red Queen = 2

Then,

$\bigstar$ 4 card of a black king and red queen in a deck of cards.

Given :

• Number of favorable outcomes = 4
• Total number of possible outcomes = 52

According to the question by using the formula we get,

$\implies\sf Probability (P) =\: \dfrac{\cancel{4}}{\cancel{52}}$

$\implies \sf\bold{\red{Probability (P) =\: \dfrac{1}{13}}}$

$\rule{150}{2}$