of the 400 doctors attending a conference 240 practice family medicine and 130 were from countries outside the US.1/3 of the family medicine practitioners were not from the US. Whats the probability that a doctor practice family medicine or is from the US? not form the US? Not a doctor, but from the US?

1 answer

From your data
F (Family doctor) = 240
I (inside the US) = 400-130= 270
FI = (2/3)(240) = 160

Make a Venn diagram using a rectangle with two overlapping circles inside, label one F and the other I
Place 160 for FI, the intersection of the two circles
Place 240-160 or 80 in the F not covered by FI
Place 270-160 or 110 in I not covered by FI
The sum of those three entries is 350, which means we have to put 50 outside the circles but inside the rectangle.

All the needed values can now be found.

( find your last part confusing, "Not a doctor, but from the US"
There is no mention of non-doctors in the 400, I assumed all mentioned as being from the US or non-US were doctors, and the remaining 400-240 were still other types of doctors than Family Practice )