1. ## Beginner probability question

At the start of flue season, Dr. Anna Ahmeed examines 50 patients over two days. Of those 50 patients, 30 have a headache, 24 have a cold, and 12 have neither symptoms. Some patients have both symptoms.

Draw a Venn diagram and determine the number of patients that have both symptoms.

How do I figure out how many have both?

2. Is the question $\displaystyle \|A\cap B\|=~?$

If so the give tells you that $\displaystyle \|\overline{A\cup B}\|=12$ (complement).

So $\displaystyle 38=\|A\cup B\|=\|A\|+\|B\|-\|A\cap B\|$.

3. Originally Posted by Plato
Is the question $\displaystyle \|A\cap B\|=~?$
Yes I believe that's what it's asking for.

Originally Posted by Plato
If so the give tells you that $\displaystyle \|\overline{A\cup B}\|=12$ (complement).

So $\displaystyle 48=\|A\cup B\|=\|A\|+\|B\|-\|A\cap B\|$.
I'm assuming you meant $\displaystyle 38 (50-12)$:

$\displaystyle 38 = \displaystyle \frac{30}{50} + \displaystyle \frac{24}{50} - \|A\cap B\|$

I can tell that looks completely wrong. Have I misunderstood something?

4. Originally Posted by IanCarney
$\displaystyle 38 = \displaystyle \frac{30}{50} + \displaystyle \frac{24}{50} - \|A\cap B\|$

I can tell that looks completely wrong. Have I misunderstood something?
It should be $\displaystyle 38 = 30 + 24 - \|A\cap B\|$.
So $\displaystyle \|A\cap B\|=30+24-38=16$ just as in the diagram.