I have a question about probability. Let’s say we have 100 homes of different ages, types and insulation levels, distributed as per the table below.
How do I determine how many homes would fall into this category: “Pre 1900-1929, 3 bed house, Solid walls, No insulation, Double glazed, Gas”
A simple probability formula gives this answer: =(70/100) * (60/100) * (50/100) * (60/100) * (70/100) * (90/100) = 7.9% = 8 homes
But this seems too low, given I know there will be several cross-overs in house types and a lot of homes will fall into the category I selected. Is there a more appropriate way of working it out?
Thanks
You need more detailed data if you want to evaluate the proportion of houses with specific characteristics.
Lets say you have information about the characteristics windows (single glazed [$sg$], double glazed [$dg$]) and heating (Gas [$G$], No Gas [$nG$]).
$\begin{array}{|c|c|c|c|} \hline & sg&dg \\ \hline G &20 &70 &90 \\ \hline nG&10 &0&10 \\ \hline &30 &70&100 \\ \hline \end{array}$
Using your method the proportion of houses with single glass [$sg$] and gas heating [$G$] is $\frac{90}{100}\cdot \frac{30}{100}=27\%$. But here the real value is $20\%$.