Maths probability question

Tim Robbins

Hi,
Say you ask 10 people to name their ten favourite movies from a choices of 100 movies. They do not have to state order.

What is the probability of overlap?

For example that all ten people pick the same 5 movies in their ten, the same 6 movies in their top ten, the same X movies in their top ten.

Or the probability that 6 people pick the same X movies? Or that 5 people pick the same X movies? Or that Y people pick the same X movies?

This is a little bit like the Birthday paradox but a bit more sophisticated.

I did a lot of Maths in college but it was a long tie ago :-)

Many thanks

MathsManiac

This is impossible to answer unless you have information on the relative popularities of the 100 movies.

(You could assume that all movies were equally likely to be in a randomly selected person's top ten, but that would be a completely unrealistic assumption.)

Tim Robbins

MathsManiac wrote: »

This is impossible to answer unless you have information on the relative popularities of the 100 movies.

(You could assume that all movies were equally likely to be in a randomly selected person's top ten, but that would be a completely unrealistic assumption.)

The assumption is that all movies are equally likely in the same way as the birthday paradox assumes each birthday of a possible 365 are equally likely.

The problem is quite simple if people just have to choose one movie, their very favourite movie. It's the same as the birthday paradox. It's more complex than that for two reasons:

1. They choose more than one movie

2. I'm look for a range of probabilities. The probability that Y people like the same X movies.