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