3 Let B be an event of a sample space S Suppose 0 SolutionGi

3. Let B be an event of a sample space S. Suppose 0

Given that 0<P(B)<1 and 0<P(B\')<1

This implies that B is a subset of universal set and B\' also and both are not null sets

i.e. BUB\' = U and Bint B equals phi.

B and B\' are mutually exclusive and exhaustive events with prob >0 but <1

Consider any set A in U.

A can also be written as A\\B UA\\B\'

Hence P(A) = P(A\\B)+P(A\\B\')-P(A\\B int A\\B\')

Or P(A) <P(A\\B)+P(A\\B\')

Hence proved.

$3. Let B be an event of a sample space S. Suppose 0 SolutionGiven that 0<P(B)<1 and 0<P(B\')<1 This implies that B is a subset of universal set and$