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Question
For an event E, write a relation representing the range of values of P(E).
Solution
The probability of an event lies between ‘0’ and ‘1’.
i.e 0 ≤ P(E) ≤ 1.
Proof: Let ‘S’ be the sample space and 'E' be the event.
Then
0 ≤ n(E) ≤ n(S)
`0/(n(S)) ≤ (n(E))/(n(S)) ≤ (n(S))/(n(S))`
or 0 ≤ P(E) ≤ 1
The number of elements in ‘E’ can’t be less than ‘0’ i.e. negative and greater than the number of elements in S.
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