# One card is drawn randomly,from a well-shuffled pack of 52 cards. then find the probability that the card drawn is

2## Answers

### This Is a Certified Answer

**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 outcomes**

**P(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 outcomes**

**P(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 outcomes**

**P(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 outcomes**

**P(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 outcomes**

**P(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 outcomes**

**P(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 outcomes**

**P(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 outcomes**

**P(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 outcomes**

**P(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 outcomes**

**P(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 outcomes**

**P(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 outcomes**

**P(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