Question

Probabilities may not be added when events are independent? True or False?

Answer 1

Definition of "independent" please? The answer is in the definition.

Answer 2

I don't have a definition...

Answer 3

A variable whose variation does not depend on that of another. Good enough?

Answer 4

Independence:
$$
\mathrm{P}(A \cap B) = \mathrm{P}(A)\mathrm{P}(B)
$$

Answer 5

That's one of the fancy ways that may or may not mean enough to anyone to solve the problem.

The very nice formula (Which @ybarrap wrote correctly and I did not) says volumes!! That is enough to answer the question.

Answer 6

Only when A and B are mutually exclusive can you add them: \(\mathrm{P(A \cup B)= P(A) + P(B)}\). Mutually exclusive events have the property: \(\mathrm{P(A\cap B) = 0}\). For two independent events, you need to use the principle of mutual exclusion to remove their intersection: \(\mathrm{P(A\cup B)=P(A)+P(B)-P(A\cup B)}\).

Answer 7

$$
\large*\mathrm{P(A\cup B)=P(A)+P(B)-P(A\cap B)}
$$
NOT
$$
\large*\mathrm{P(A\cup B)=P(A)+P(B)-P(A\cup B)}
$$
In last line.

Answer 8

Inclusion-Exclusion Principle (not mutual exclusion principle):
http://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle

Answer 9

true

Answer 10

I keep thinking it's false

Answer 11

Independent events may NOT be added, generally, because although they are independent, they are not (generally) mutually exclusive, which is the case were you can just add them.

Answer 12

So true