Three Times the Probability Question

[SwAnK]

hey, i came upon this question in the textbook " for what probability will an event be three times as likely to occur than not to occur?" I'm not really sure how to even go about this question so any hints or help would be appreciated
-thanks

 

[matt grime]

Let p be the probability of occurrence, q the probability of nonoccurence. We are told p=3q from the question, and all we need to do is find another condition. Which is...?

 

[SwAnK]

i understand p=3q, meaning the probability is three times more likely to occur than not but what do you mean by another condition? Like the probability of something being 3 times as likely to NOT occur than to occur?

 

[matt grime]

No. If the probability of X is p, and the probability of not X is q, then what condition does this impose on p and q?

 

[verty]

How do you express a probability?

 

[Fredrik]

i understand p=3q, meaning the probability is three times more likely to occur than not but what do you mean by another condition? Like the probability of something being 3 times as likely to NOT occur than to occur?

What Matt said means that you must express q as a function of p. Then you must solve the equation p=3q for p to find your answer.

 

[matt grime]

I meant no such thing. You can't 'solve' p=3q. I meant precisely what I said. Find two relationships between p and q. (Hint: LAW OF TOTAL PROBABILITY, or in this case if A happens with probability p, then NOT(A) happens with probability 1-p)

 

[Fredrik]

Now you're not making much sense at all. I assumed that you meant that he should realize that q=1-p. That turns p=3q into p=3(1-p), and you can definitely solve that for p. So why are you objecting? Is that something that you just do by default?

And why are you talking about two relationships between p and q?! He already knows that p=3q, so there's only one relationship left to find and that's q=1-p.

 

[matt grime]

Yes, I meant that the OP should notice that 1-p=q. It was not at all clear that that was what you were referring to. You said to express p as a function of q. Well, p=3q does precisely that, modulo the fact we don't actually really need to invoke the word function at all. Your post seemingly refers to only one relation between p and q, since it invokes a relation and gives p=3q and doesn't indicate that by these you mean different relations. The point is to find two. You don't mention this at all, hence my confusion as to what you thought you were adding to the debate.

 

[Fredrik]

You said to express p as a function of q. Well, p=3q does precisely that, modulo the fact we don't actually really need to invoke the word function at all.

That's a good point actually.

(I said express q as a function of p, but p=3q does that too, so you're still right).