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

Answer:

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

Step-by-step 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:

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