RESULT 1

Consider the set S of all possible outcomes of an experiment or a trial. A set of this kind sometimes called a Probability space or Sample space. Any event A can be represented by the subset of S, which contains all the outcomes in which the event occursLet S contains a finite number of equally likely outcomes, say m, so that n(S) = n. Let the event A has m sample points so that n(A) = m.

We have

P(A) = n(A)/ n(S) = m/n

= Number of Favourable Outcomes

Number of Possible Outcomes

Since A is a subset of S,

Hence 0

**≤ P(A)****≤ 1**Note: The probability of an event A is a number between 0 and 1 inclusive. If P(A) = 0, then the event cannot possibly occur.

If P(A) = 1, then the event is certain to occur.

RESULT 2

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Let A denote the event 'A does not occur'

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Now P(A) = n(A) /n(S) = n-m = 1-m

n n

= 1 - P(A)

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Therefore P(A) = 1 - P(A)

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This implies P(A) + P(A) = 1

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