In my intro probability/stats class, we were given the following problem: A restaurant owner would like to know how frequently his guests attend his restaurant. Based on an online survey, he is given the following information:
- 80% went in the last 3 months
- 48% went in the last month
- 25% went in the last 2 weeks
- 14% went in the last 7 days
The problem is: say 1000 people attend his restaurant. How many of these 1000 attended in the last 7 days, 2 weeks, month, and 3 months.
I thought initially that this was a simple multiply 1000 by the percentages above, but as you can see, they do not add to 100. My secondary thought was to normalize these perhaps, so it's not 80%, but 0.80 / (0.80 + 0.48 + 0.25 + 0.14), not 48%, but 0.48/(0.80 + 0.48 + 0.25 + 0.14), and so forth, so you get: [0.47, 0.287, 0.1497, 0.08], which now do add to 100, and you get some sensible answers. But, I don't know why this should work, or if it is the correct approach?