# For every person who actually has the flu, there are 6 persons who have flu-like symptoms resulting from a cold. If a doctor sees 40 patients, write and solve a proportion to determine how many of these you would expect to have a cold?

Oct 28, 2016

$34 \frac{2}{7} \text{ }$ This is an unexpected proportion. Is the question correct?
I suppose you could round this up to 35 people

#### Explanation:

Breaking the question down into component parts:

For every person $\to 1$
There are -> 1+?
6 persons $\to 1 + 6$

Note that the question wording is very specific about the proportions.

It is declared that the number of people with flue like symptoms due to a cold is 6.

It is also declared that the corresponding number of people with genuine flue is 1

................................................................................

Combined count of people with genuine flue symptoms and those with flue like symptoms is 1 + 6 = 7

This gives the fractional proportion of $\frac{1}{7}$ that probability suggests have flue.

Note that probability (statistics) is not certainty. It is a strong indicator.

So the expected proportion of genuine flue cases from 40 patients is: $\frac{1}{7} \times 40$

Thus those that probably have a cold is

$\left(1 - \frac{1}{7}\right) \times 40 \text{ " ->" " 6/7xx40" "=" } 34 \frac{2}{7}$ people

$\textcolor{g r e e n}{\text{You can not have "2/7" of a person so perhaps the counts of the }}$$\textcolor{g r e e n}{\text{people in the question are wrong.}}$