Discuss the validity of the following statement. If the statement is always true, explain why. If not, give a counterexample.

Question

4 years ago

10

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.

Mathematics

1 answer:

Zigmanuir [339] · Answer 1 · 2021-12-27T18:24:55+03:00

Zigmanuir [339]4 years ago

3 0

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:

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

Discuss the validity of the following statement. If the statement is always​ true, explain why. If​ not, give a counterexample.

Discuss the validity of the following statement. If the statement is always true, explain why. If not, give a counterexample.