1

Suppose there are 15 males and 25 females, a total of 40. I am trying to show that the probability of a person being male given that they're female is an independent event. Obviously, the two events can't happen at the same time, which suggests their independence, but I'm a little confused on how to prove this mathematically.

The rule for independent events is that: $P(A \cap B) = P(A)$.

So here's what I did: $$P(\text{male} \cap \text{female}) = 0$$ $$P(\text{male}) = \frac{15}{40}$$

But then $P(A \cap B) \neq P(A)$, which means it should be dependent when it's not!

Am I misunderstanding something here?

Niko
  • 73
  • 1
    You are conflating disjointness and independence. The intuition is that knowing someone is female gives you a lot of information about whether they are male, so they are very dependent. See this discussion. – angryavian Sep 18 '22 at 16:14
  • So to clarify, does that mean that the two disjoint events of being male and female are actually dependent? My initial intuition of independence is whether or not they can happen at the same time, so I guess that's flawed. – Niko Sep 18 '22 at 16:28
  • Indeed. Moreover, "the rule for independent events" is not what you wrote. – Anne Bauval Sep 18 '22 at 16:45
  • Oops. I meant to say P(A/B), tho the equations will still be the same. Thanks! – Niko Sep 18 '22 at 16:49

0 Answers0