Question

For an event E, write a relation representing the range of values of P(E).

Answer 1

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.