Basic numeracy-probability

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Basic numeracy, probability

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Basic numeracy-probability

  1. 1. Click Here to Join Online Coaching Click Here www.upscportal.com Basic Numeracy
  2. 2. www.upscportal.com Click Here to Join Online Coaching Click Here Probability Probability Probability is used to indicate a possibility of an event to occur. It is often used synonymously with chance. (i) In any experiment if the result of an experiment is unique or certain, then the experiment is said to be deterministic in nature. (ii) If the result of the experiment is not unique and can be one of the several possible outcomes then the experiment is said to be probabilistic in nature. Various Terms Used in Defining Probability (i) Random Experiment: Whenever an experiment is conducted any number of times under identical conditions and if the result is not certain and is any one of the several possible outcomes, the experiment is called a trial or a random experiment, the outcomes are known as events. .
  3. 3. www.upscportal.com Click Here to Join Online Coaching Click Here eg, When a die is thrown is a trial, getting a number 1 or 2 or 3 or 4 or 5 or 6 is an event. (ii) Equally Likely Events: Events are said to be equally likely when there is no reason to expect any one of them rather than any one of the others. eg, When a die is thrown any number 1 or 2 or 3 or 4 or 5 or 6 may occur. In this trial, the six events are equally likely. (iii) Exhaustive Events: All the possible events in any trial are known as exhaustive events. eg, When a die is thrown, there are six exhaustive events. (iv) Mutually Exclusive Events: If the occurrence of any one of the events in a trial prevents the occurrence of any one of the others, then the events are said to be mutually exclusive events. eg, When a die is thrown the event of getting faces numbered 1 to 6 are mutually exclusive.
  4. 4. www.upscportal.com Click Here to Join Online Coaching Click Here Classical Definition of Probability If in a random experiment, there are n mutually exclusive and equally likely elementary events in which n elementary events are favourable to a particular event E, then the probability of the event E is defined as P (E)
  5. 5. www.upscportal.com Click Here to Join Online Coaching Click Here Addition Theorem on Probability If El and E2 are two events in a sample space S, then P (El U E2) = P (El) + P (E2) – P (El ∩ E2). If E1 and E2 are mutually exclusive events (disjoint), then P(El U E2) = P (El) + P (E2) .
  6. 6. www.upscportal.com Click Here to Join Online Coaching Click Here Independent and Dependent Events Two or more events are said to be independent if the happening or non-happening of any one does not depend (or not affected) by the happening or non-happening of any other. Otherwise they are called dependent events. eg, Suppose a card is drawn from a pack of cards and replaced before a second card is drawn. The result of the second drawn is independent of the first drawn. If the first card drawn is not replaced, then the second drawn is dependent on the first drawn. If El and E2 are independent events, then P(El ∩ E2) = P(El) × P(E2) Simple Event An event which cannot be further split is called a simple event. The set of all simple events in a trial is called a sample space.
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  8. 8. www.upscportal.com Click Here to Join Online Coaching Click Here ‘Smart’ Facts • When a die is rolled six events occur. They are {1, 2, 3, 4, 5 and 6} • When two dice are rolled 36 events occur. They are [(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)] • When a coin is tossed 2 events occur. They are {H, T} • When two coins are tossed 4 events occur. They are {HH, HT, TH, T T} • When three coins are tossed 8 events occur. They are {HHH HHT, HTH, HT T, T HH, THT, T TH, T T T} • In a pack of 52 cards there are 26 red cards and 26 black cards. The 26 red cards are divided into 13 heart cards and 13 diamond cards. The 26 black cards are divided into 13 club cards and 13 spade card. Each of the colours, hearts, diamonds, clubs and spades is called a suit. In a suit, we have 13 cards (ie, A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3 and 2)
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