[bo1024]

If you understand problem 2, then you will get problem 3 as well, so let's focus on 2.

> It is right that probability = favaroble out comes / total possible outcomes.

No, not actually: It is only right if all outcomes are equally likely! (There's an old joke about the guy who has a 50% chance of winning the lottery, since either he will win it or he won't.)

In particular, you make that mistake here:

> 1) Potential Outcome 1: Both are boys 2) Potential Outcome 2: One boy and one girl 3) Potential outcome 3: Both are girls

These three outcomes are not all equally likely. Outcome 1 has probability 1/4, outcome 2 has probability 1/2, and outcome 3 has probability 1/4. (This is if you assume that each child has a half chance each of being a boy/girl.)

Norvig gets rid of this problem by listing out all four possible outcomes, which are all equally likely.

1. First child boy, Second child boy

2. First child boy, Second child girl

3. First child girl, Second child boy

4. First child girl, Second child girl

[mamon]

Again, both Norvig and you are messing with ordering of events. If you list 4 events like this, assuming that ordering of boys and girls matters, then you should stick with that. So, if ordering mattered when children were born it should also matter when you are doing "checks". So you shouldn't formulate problem as "one of the children is boy", you should formulate problem as "first child is boy" (with ordering in place), which eliminates possibility 3. Otherwise you are "solving" problem by listing sample space of completely different problem.

[bo1024]

The event "at least one child is a boy" is well-defined on the 4-state sample space. It is the set of events (first boy/second boy, first boy/second girl, first girl / second boy). It has probability 3/4.