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 = 52C1
=
52
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.
Solution Ans : (a)
1
13
, 1 : 12, (b)
1
4
, 1 : 3

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
13
, 4 : 9

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
13
, 11 : 2

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:
  1. The card is a king or a queen.
  2. Getting a number card.
  3. red or black
  4. Either a face card (jack, queen, king) or a six.
  5. At least a spade or a king
  6. Getting a queen of a club or king of heart
  7. Either a red or a numbered card
  8. Either black or an ace
  9. Neither a spade nor a heart.
Solution Ans : [8, 40, 52, 16, 16, 2, 46, 28, 26]

Practice Problems

  1. Find the probability of getting diamond, when a card is drawn from a pack
  2. Find the probability of getting an ace, when a card is drawn from a pack of 52 cards
  3. When a card is drawn at random from a pack, find the probability that it may be either king (or) queen
  4. Find the probability of drawing a card which is not a diamond from a pack of 52 cards
  5. Probability of drawing and not drawing a spade in a single draw is:
  6. The odds in favour of drawing a king or a diamond from a well shuffled pack of cards are

  7. 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:

    1. Getting a diamond
    2. Either a spade or a queen
    3. Neither a hearts nor a club
    4. Either a heart or a queen
    5. Either a face card or a diamond card
    6. Not a diamond card
    7. Drawing a king or a diamond
    8. An ace of clubs
    9. One of the court cards (Jack or queen or king)
    10. A two of a heart or a diamond
    11. A black card.
    12. Red or king
    13. Either a Queen or a Jack?
Author : The Edifier
Page PS5