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?

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Answer 1 · 2016-10-28T19:01:51

$34 2/7" "$ This is an unexpected proportion. Is the question correct?
I suppose you could round this up to 35 people

Breaking the question down into component parts:

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

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 $1/7$ 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: $1/7xx40$

Thus those that probably have a cold is

$(1-1/7)xx40" " ->" " 6/7xx40" "=" "34 2/7$ people

$color(green)("You can not have "2/7" of a person so perhaps the counts of the ")$ $color(green)("people in the question are wrong.")$