Suppose the A B and C are not mutually exclusive Use appropr

Suppose the A, B, and C are not mutually exclusive. Use appropriate appropriate arguments to show that

Solution

this is very simple

as the problem say that A,B and C are not mutually excluvise that means that they can have interception

so with the union of 3 events we are going to subctract the interception of A and B , B and C , A and C

so that will be a number ok?

but with the sum P(A)+P(B)+P(C) we are only taking the value of the event , so if we sum P(A) + P/(B) for example we are summing the interception of P(A and B) because the interception is in the 2 events so we are summing that value that the union of the 3 events dont have for that reason

the union is lower than the sum of 3 events