Here's a probability question I've been wondering. Suppose there's a company that has a million customers. It is known that 55% of these customers are male and 45% of customers are female. Task is to guess the sex of the next 100 (of the existing) customers who are going to visit the company. For every right guess point is awarded. What's the best strategy to get most correct answers?
If we consider the customers one by one, it is good plan to always guess the most probable answer and therefore guess that all 100 of the customers are male. However if we take the hundred people as a group, isn't this task analoguous to situation where one litre of seawater in a container has same salinity as seawater in general? Therefore we could guess that there are 55 males and 45 females among the group of 100 customers. Certainly, if instead of 100 people we would take the whole million customers as a group then 55%/45% split would be the true and correct answer.
My question is this: what changes the way of thinking between individuals and groups? Which is the correct way to think about this problem?