Question about independence

There is this quiz question in the lecture: “In a school with 100 kids, where 50 like soccer and 50 don’t, if we randomly split the kids in two rooms with 50 kids each, what is your best estimate on the number of kids in room 1 that like soccer?” and the answer is 25.

Can you help me understand this? Why 25 kids in room 1 that like soccer is more likely than 24 kids in room 1 that like soccer for example?

It’s a joint probability question. If you have two independent events, their joint probability is the product of the individual probabilities.

The two independent events in this example are:

  • whether a kid likes soccer. Its probability is 50/100, or 0.5.
  • which room a kid is placed in. There are two rooms, so that probability is 1/2, or 0.5.

The joint probability is (0.5 * 0.5) = 0.25, or 25 out of 100.

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Got it, thank you!