Question

Discuss the validity of the following statement. If the statement is always​ true, explain why. If​ not, give a counterexample. If Upper P (Upper E )plus Upper P (Upper F )equals Upper P (Upper E union Upper F )plus Upper P (Upper E intersect Upper F )​, then E and F are mutually exclusive events.

Answer 1

`P(E \cup F)=P(E)+P(F)`.

Explanation:

Given the statement

If
`P(E)+P(F)=P(E \cup F)+P(E \cap F)`, then E and F are mutually exclusive events.

If two events are mutually exclusive, they have no elements in common. Thus, P(E∩F)=0.

Therefore, the statement is always true as P(E∩F)=0

For mutually exclusive events:

`P(E \cup F)=P(E)+P(F)`.