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Probability

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Probability is a numerical description of how likely an event is to occur or how likely it is that a proposition is true. Probability is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility, and 1 indicates certainty. 

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Probability – 7 Tricks to solve problems on Balls and bags-Part 1

Probability – 7 Tricks to solve problems on Balls and bags-Part 2

Please Read the below formula and concept every time before you start to solve the questions.

  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:
    1. Rolling an unbiased dice.
    2. Tossing a fair coin.
    3. Drawing a card from a pack of well-shuffled cards.
    4. Picking up a ball of a certain colour from a bag containing balls of different colours.
    Details:
    1. When we throw a coin, then either a Head (H) or a Tail (T) appears.
    2. 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.
    3. 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 in each unit. There are Kings, Queens and Jacks. These are all called face cards.
  3. Sample Space: When we perform an experiment, then the set S of all possible outcomes is called the sample space.Examples:
    1. In tossing a coin, S = {H, T}
    2. If two coins are tossed, the S = {HH, HT, TH, TT}.
    3. 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.
  5. The probability of Occurrence of an Event: Let S be the sample and let E be an event. Then, E  S.
     P(E) = n(E) .
    n(S)
  6. Results on Probability:
    1. P(S) = 1
    2. 0  P (E)  1
    3. P() = 0
    4. For any events A and B we have : P(A  B) = P(A) + P(B) – P(A  B)
    5. If A denotes (not-A), then P(A) = 1 – P(A).