Probability

What is an experiment ?

1. Experiment: An operation which can produce some well-defined outcomes is called an experiment.

2.Random Experiment: An experiment in which all possible outcomes are known and the exact output cannot be predicted in advance, is called a random experiment.

 

Examples of performing a Random Experiment

Examples of Performing a Random Experiment:

  1. Rolling an unbiased dice.
  2. Tossing a fair coin.
  3. Drawing a card from a pack of well-shamed curds.
  4. Picking up a ball of a certain color from a bag containing balls of different
    colors.

Details:

  1. When we throw a coin. Then either a Head (H) or a Tail (T) appears.
  2. Dice is a solid cube, having 6 faces, marked 1,2,3,4,5,6 respectively when we throw a die, the outcome is the number that appears on its upper face.
  3. A pack of cards has 52 cards.
    1. It has 13 cards of each suit, namely Spades, Clubs, Hearts and Diamonds.
    2. Cards of spades and clubs are black cards.
    3. Cards of hearts and diamonds are red cards.
    4. There are 4 honors of each suit.
    5. These are Aces, Kings, Queens and Jacks.
    6. These are called face cards.

Sample Space

  1. Sample Space: When we perform an experiment, then the set S of all possible outcomes is called the Sample Space.
    1. Examples of Sample Spaces :
      1. In tossing a coin, S={H, T}
      2. if two coins are tossed then S= {HH,HT,TH,TT},
      3. In rolling a dice, we have, S={1, 2, 3, 4, 5, 6},