Question

If two events are independent, then Group of answer choices the sum of their probabilities must be equal to one. they must be mutually exclusive. their intersection must be zero. None of the above.

Answer 1

Answer:

For this case we can define the following two events A and B.

In order to classify A and B as independent we needd to satisfy this condition:

$P(A \cap B) = P(A) *P(B)$

None of the above.

True, because none of the options were correct.

See explanation below

Step-by-step explanation:

For this case we can define the following two events A and B.

In order to classify A and B as independent we need to satisfy this condition:

$P(A \cap B) = P(A) *P(B)$

So let's analyze one by one the possible options:

the sum of their probabilities must be equal to one.

False, the sum of the probabilities can be <1 so this statement is not true

they must be mutually exclusive.

False when we talk about mutually exclusive events we are saying that:

$P(A \cap B) =0$

But independence not always means that we have mutually exclusive events

their intersection must be zero.

False the intersection of the probabilities is 0 just if we have mutually exclusive events, not independent events

None of the above.

True, because none of the options were correct.