# Drawing/Picking/Selecting/Choosing Two/Three/More Cards from a well shuffled Pack of Cards

# Problem 1

In drawing 2 cards from a pack of cards, the total number of possible out comes

# Solution

Total number of cards in the pack

= 52

Number of cards drawn

= 2

**Experiment** :

Drawing 2 cards from the pack of cards

Total Number of Possible Choices

= Number of ways in which 2 cards can be drawn from the 52 cards

⇒ n | = | ^{52}P_{2} | ||

= |
| |||

= | 26 × 51 | |||

= | 1,326 |

# Problem 2

Three cards are drawn from a pack of 52 cards. The probability that they are a king, a queen and an even numbered cards is

Solution Ans :

16 |

1,105 |

# Problem 3

If 7 cards are drawn at random. From a pack of 52 cards then find the probability that 3 of them are red and 4 are black.

Solution Ans :

2,875 |

5,593 |

# Problem 4

From a pack of cards, 2 cards are chosen at random. Find the probability of the event of getting a 10 not of hearts and another hearts cards.

Solution Ans :

6 |

215 |

# Problem 5

A pack of cards contain 4 aces, 4 kings, 4 queens and 4 jacks. Two cards are drawn at random. the probability that at least one of them is an ace is

Solution Ans :

6 |

215 |

# Problem 6

From a pack, two cards are drawn, the probability that either both are black of both are queen is

Solution Ans :

331 |

1,326 |

# Problem 7

If two cards are drawn from a pack of 52 cards, then the probability that they belong to the same suit is

Solution Ans :

4 |

17 |

# Problem 8

Five cards are drawn at random from a pack. The probability that four of them may have the same face value is

Solution Ans :

1 |

833 |

# Problem 9

Define the Event and identify the number of favourable choices in the following

- From a normal pack of cards 4 are drawn. Find the probability that they are different suits?
- While shuffling a pack of 52 cards, 2 are accidentally dropped. Find the probability for two missing cards to be of different colours (colors may be taken as red and black)
- Two cards are drawn simultaneously from a pack. The probability that at least one of them will be the ace of hearts is
- Two cards are drawn from a pack. Find the probability that one of them is a club and the other is not a club.
- Two cards are drawn simultaneously from the same set. Find the probability that none of them will be the ace of spade

Solution Ans : 1) 28,561, 2) 676, 3) 51, 4) 1,275, 5) 507

# Practice Problems

- Two cards are drawn from a pack, the probability of getting a king and a queen is
- Three cards are drawn from a pack of 52 cards. The chance that they are an ace a king and a queen is
- Two cards are drawn from a pack. Find the probability that one of them is a club and the other is not a club.
- Find the probability of getting two hearts when two cards are drawn from a pack.
- If 2 cards are drawn from a pack of cards, then find the probability of getting at least one club.
- From a pack of 52 cards, four cards are drawn. Find the chance that they will be four of the same suit?
- Four cards are drawn in succession from a pack of cards without replacement. What is the probability that they are all aces?

Author : The Edifier