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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.

Respuesta :

Answer:

[tex]P(E \cup F)=P(E)+P(F)[/tex].

Step-by-step explanation:

Given the statement

If [tex]P(E)+P(F)=P(E \cup F)+P(E \cap F)[/tex], 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:

[tex]P(E \cup F)=P(E)+P(F)[/tex].

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