"at least probabilities"

#1
Okay, I've been struggling with this problem for over two hours and I'm continuing to get more confused. Any advice would be great.

Here's the problem:

The probability of flu symptoms for a person not receiving any treatment is 0.035. In a clinical trial of a common drug used to lower cholesterol, 38 of 1021 people treated experienced flu symptoms. Assuming the drug has no effect on the likelihood of flu symptoms, estimate the probability that "at least" 38 people experienced flu symptoms.


I know for "at least" probabilities you find the complement, but since the question isn't asking for the opposite of having flu symptoms, would I still use it? Plus, my dealings with "at least" probabilities have dealt with "at least 1" where I use 1-P. How do I figure "at least 38"?
 

Dason

Ambassador to the humans
#2
I know for "at least" probabilities you find the complement, but since the question isn't asking for the opposite of having flu symptoms, would I still use it? Plus, my dealings with "at least" probabilities have dealt with "at least 1" where I use 1-P. How do I figure "at least 38"?
Well you can use the complement and it does make some calculations easier... you aren't finding the correct complement. Specifically you're interested in:

[math]P(X \geq 38)[/math] the trick to using the complement is to recall that if A is an event then [math]P(A) = 1 - P(A^c)[/math] (where [math]A^c[/math] is the complement of A)

so we're really looking for the complement of {X >= 38}. Well if we aren't in the set X >= 38 then that means that X must be less than 38 so the complement is {X < 38} so using this

[math]P(X \geq 38) = 1 - P(X < 38)[/math]

Now if that actually helps depends on what you know and what you can calculate easily...