According to the article sumwun so graciously offered, it differs depending on what version of the game you have. If you have the Japanese version of Crystal, your odds are as follows:
In the Japanese version of Pokémon Crystal, there is a 50% chance the hatched Pokémon will be Shiny (IVs 2/10/10/10) and a 50% chance it will not (IVs 0/0/0/0).
This results in a 7.142857…% chance of any of the following:
- Pichu
- Shiny Pichu
- Cleffa
- Shiny Cleffa
- Igglybuff
- Shiny Igglybuff
- Tyrogue
- Shiny Tyrogue
- Smoochum
- Shiny Smoochum
- Elekid
- Shiny Elekid
- Magby
- Shiny Magby
Now, if you have the international version (anything other than Japanese) of Crystal, the chances are as follows:
- Pichu, 8%
- Shiny Pichu, 1%
- Cleffa, 16%
- Shiny Cleffa, 3%
- Igglybuff, 16%
- Shiny Igglybuff, 3%
- Tyrogue, 8%
- Shiny Tyrogue, 1%
- Smoochum, 14%
- Shiny Smoochum, 2%
- Elekid, 12%
- Shiny Elekid, 2%
- Magby, 10%
- Shiny Magby, 2%
Hope I helped!
Source