Trick probability question. Are A and B independent events?

Question

A person is chosen at random from a large population containing 50% males and 50% females.

A – event that the person is male
B – event that the person is female

Are A and B independent events? Justify your answer.
Do you find this answer rather unintuitive? Explain.

I meant TRICKY probability question.

I meant the question exactly as worded. Except for tricky instead of trick.

Answer 1

No they are not independent, because if we know B happened, for sure A has not happened.

Do you mean drawing two people from the population?
P( 2nd person female/ first male)?
Since the population is large, we can assume independence.

EDIT: No Dr D, they are not independent, they are multually exclusive and mutually exclusive events is a very strong case of dependence, becuase the happening of one automatically means the other has not happened.

Answer 2

Going off of what Christine said...

...If A and B are independent, then we would expect that P(A and B)=P(A)P(B). Assuming independence, P(A and B) would be 1/4. However what is the probability of choosing a person at random from this population such that that person is male AND that that person is female--0-- because a person couldn't be both (for the purposes of this problem).

Answer 3

A and B are not independents.

Two events are said to be independent if the result of the second event is not affected by the result of the first event.

If A and B are independent events, the probability of both events occurring is the product of the probabilities of the individual events
If A and B are independent events,
P(A and B) = P(A) x P(B).

Answer 4

That's tricky... wouldn't it depend on the question?

What if a male had left the population?

What if a female left the population?

What if one of the males or females die?

If we are to chose one guy/girl out of the blues, it would definitely be independent (could be wrong), but if we are to choose one after another, the girl would depend on the male or the male would depend on the female population.
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Independent is usually used for picking 2 things one after another so I don't think it's valid to use "independent events" for something such as a single pick.
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EDIT: Are you tricking me? Lol this is tricky.

Answer 5

Very simple; they're not independent, they are mutually exclusive. Indeed, they are complementary.

I don't find this unintuitive; I would find it unintuitive to think that whether or not a person is male has no bearing on whether or not they are female!