(I'm Overwhelmed) Data Analysis Progress Quiz #10 - Q12

[user7951]

don’t understand why the minimum is 0.1 and not 0.

There seems to be no indication in the question that this not not the lower case of mutual exclusive for A and B (or P and Q in this case), ie Prob= 0.

[Kweku]

The two Probabilities must sum to maximum 1.

If we use 0, they Prob sum to 1.1, which is more than 1.

[user7951]

Thanks for the answer.

but I was asking about the minimum for “the smallest possible probability of P and Q”

this usually would be 0 as for A and B mutually exclusive = 0.

But the answer provided is 0.1.

[Kweku]

Yes. My answer still applies.

If the minimum is 0, the probabilities will sum to 1.1 which cannot happen.

So at a minimum, the minimum for both should be 0.1 so that now the probabilities can sum to max 1.

[user7951]

Thanks for the speedy reply.

Could you provide a link to where this exact principle was covered?

I don’t recall this scenario at all.

[cylverixxx]

Problem Modification

Well you can start by noting that the following holds from our axioms: \mathbb{P}(A \cup B) = \mathbb{P} (A) + \mathbb{P} (B) - \mathbb{P} (A \cap B) \leq 1 This can be equivalently written as follows: \mathbb{P} (A \cap B) \geq \mathbb{P} (A) + \mathbb{P} (B) -1 You also know that \mathbb{P} (...) \geq 0, and so it’s fair to surmise that the lower bound would be 0 if the individual probabilities add to less than (or equal to) 1. Otherwise, the minimum would be the “amount” by which the s…

I’m not sure where that’s covered, but if you just want an answer to your question, you can read my answer here. I’ve addressed your concerns in that post.