Maths formulas # 04 :)


PROBABILITY

  1. Experiment:
An operation which can produce some well-defined outcomes is called an experiment.
  1. Random Experiment:
An experiment in which all possible outcomes are know and the exact output cannot be predicted in advance, is called a random experiment.
Examples:
  • Rolling an unbiased dice.
  • Tossing a fair coin.
  • Drawing a card from a pack of well-shuffled cards.
  • Picking up a ball of certain colour from a bag containing balls of different colours.
Details:
  • When we throw a coin, then either a Head (H) or a Tail (T) appears.
  • A 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.
  • A pack of cards has 52 cards.
  • It has 13 cards of each suit, name Spades, Clubs, Hearts and Diamonds. 
  • Cards of spades and clubs are black cards. 
  • Cards of hearts and diamonds are red cards. 
  • There are 4 honours of each unit. 
  • There are Kings, Queens and Jacks. These are all called face cards.
  1. Sample Space:
When we perform an experiment, then the set S of all possible outcomes is called thesample space.
Examples:
  • In tossing a coin, S = {H, T}
  • If two coins are tossed, the S = {HH, HT, TH, TT}.
  • In rolling a dice, we have, S = {1, 2, 3, 4, 5, 6}.
   4. Event:
                  Any subset of a sample space is called an event.
  1. Probability of Occurrence of an Event:
Let S be the sample and let E be an event.
 P(E) =
n(E)
.
n(S)


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