# Drawing/Picking/Choosing Single/One Card from a Pack - Probability - Problems & Solutions

# Problem 1

What is the total number of possible choices in the experiment of drawing a card from a pack of cards.

# Solution

In the experiment of drawing a card from a pack of cards

The total number of possible choices

= Number of ways in which one card can be drawn from the total 52 cards

⇒ n | = | ^{52}C_{1} | ||

= |
| |||

= | 52 |

# Problem 2

If a card is drawn from a pack of cards, then find the probability and odds for the card to be (a) an ace and (b) a club.

# Problem 3

If a card is drawn at random from a pack of cards, find the probability and odds that the card is either a spade or a king.

Solution Ans :

, 4 : 9

4 |

13 |

# Problem 4

From a normal pack of cards, a card is drawn at random. Find the probability and odds of not getting a jack or a king.

Solution Ans :

, 11 : 2

11 |

13 |

# Problem 5

A card is drawn from an ordinary pack and a gambler bets that it is a spade or an ace. What are the odds against his winning this bet?

Solution Ans : 9 : 4

# Problem 6

Define the Event and identify the number of favourable choices in the following cases which relate to the experiment of drawing a card from a pack of cards:

- The card is a king or a queen.
- Getting a number card.
- red or black
- Either a face card (jack, queen, king) or a six.
- At least a spade or a king
- Getting a queen of a club or king of heart
- Either a red or a numbered card
- Either black or an ace
- Neither a spade nor a heart.

Solution Ans : [8, 40, 52, 16, 16, 2, 46, 28, 26]

# Practice Problems

- Find the probability of getting diamond, when a card is drawn from a pack
- Find the probability of getting an ace, when a card is drawn from a pack of 52 cards
- When a card is drawn at random from a pack, find the probability that it may be either king (or) queen
- Find the probability of drawing a card which is not a diamond from a pack of 52 cards
- Probability of drawing and not drawing a spade in a single draw is:
- The odds in favour of drawing a king or a diamond from a well shuffled pack of cards are
Define the Event and identify the number of favourable choices in the following cases which relate to the experiment of picking a card from a pack of cards:

- Getting a diamond
- Either a spade or a queen
- Neither a hearts nor a club
- Either a heart or a queen
- Either a face card or a diamond card
- Not a diamond card
- Drawing a king or a diamond
- An ace of clubs
- One of the court cards (Jack or queen or king)
- A two of a heart or a diamond
- A black card.
- Red or king
- Either a Queen or a Jack?

Author : The Edifier