S1 Q

[WhoTookMyUsername]

Did this come up on the real UMAT?

Let's say there's 1000 people, each with a 50% chance of having diabetes and each with 25% chance of having asthma
which is more likely
a) 125 people have diabetes and asthma
b) less than 500 people have diabetes


Because of sampling errors, having EXACTLY 125 people with diabetes and asthma is LESS likely than 1000 people having diabetes IMO.
Am i reading too much into this?
Should you assume that the percentages are theoretically perfect and not randomly account for sampling error?


2)
Should you take into consideration that if there is a 50% chance of having diabetes and a 25% chance of having there is a less than 75% chance of having one of diabetes or asthma IF you are just comparing the likelyhood of one or the other to the likelyhood of one of another 2 options?

e.g.
what has a higher likelyhood
a random person with asmthma or diabetes
or
a random person with obesity (40%) and diarrhea (50%)

Is it OK for these relative comparisons to just add the percentages?
When in general can you just add percentages and when should you multiply individual chance?

thanks

[BlueSky_3]

I don't really get what you're trying to ask, but for your first example you are in a sense thinking too deeply, since you have to only use information they give you and so (a) should be right. And for the second example, again I don't understand why you thought of adding percentages when you want the intersection of those two events, so multiplying the probabilities and doing so will give a greater chance of having obesity and diarrhea. 

[WhoTookMyUsername]

well often adding the percentages is much quicker and easier, and in some cases it still gives the correct result (when precentages are similar i think); but what cases exactly can you do this in?

[BlueSky_3]

I think I get what you mean now, its simply that bigger numbers, whether added or multiplied produce larger numbers than smaller ones but I don't think adding will produce the same results if the percentages are similar .

[WhoTookMyUsername]

bump,
others have any thoughts?
thanks