? about an example in High Yield BS

[Mystique]

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So in the 2nd edition of HY BS on pg 112 Example 23-2, they ask a probability ?, and I can't seem to make sense of it. I'm rather embarassed to ask 😳 , but I guess here is a good a place as any.

"After 2 years of clinical trials, it is determined that 20% of patients who take a new drug for hypertension develop nausea. If two patients (patients A and B) take the drug, calculate the following:

At least one patient (i.e., either A or B or both A and B) will experience nausea."

Ok, so I know to get either A or B it's simply .2+.2=.4
I also know that both A and B is .2*.2=.04

What I can't seem to get through my thick skull is why you subtract the .04 from .4 rather than add the two #s together.

I guess it's the "or" that's throwing me off. Can someone explain why the answer is 0.36 instead of 0.44? Thanks. 😳

 

[Radiohead]

The question asked: what is the chance that "at least" one of the pts would develop nausea?
So, since there is an 80% chance that each individual wouldn't get nauseated, you take .80 squared=.64. That is the chance that neither A nor B would have the side effect. So, 1-.64=.36, that is the probablility that at least one would get sick. Remember that the answer includes the chances of both one and two sick people. You can work these problems out using an approach similar to the Hardy-Weinberg equation where p=.8 and q=.2

I hope this helps

 

[Mystique]

The question asked: what is the chance that "at least" one of the pts would develop nausea?
So, since there is an 80% chance that each individual wouldn't get nauseated, you take .80 squared=.64. That is the chance that neither A nor B would have the side effect. So, 1-.64=.36, that is the probablility that at least one would get sick. Remember that the answer includes the chances of both one and two sick people. You can work these problems out using an approach similar to the Hardy-Weinberg equation where p=.8 and q=.2

I hope this helps

This makes perfect sense! I should have just worked it out using HW; it would have been so much simpler than the way HY was trying to go about solving it. Thank you so much for your help, Radiohead. Muchas gracias. 🙂