basic numeracy-probability

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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.

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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.



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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)



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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) .



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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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‘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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