Female and shiny starter pokemon

The other day I was playing pokemon and I remembered some time ago my brother had told me starter pokemon were much less likely to be female. This led me to think if the probability of getting a shiny starter pokemon was less than any other pokemon’s chance.

I went online and I found out that the probability of getting a shiny starter was the same as any other pokemon, 0.0122%. Also, the probability of getting a female starter is 12.5%; almost 1000 times more than getting any shiny.

After this, I wondered: what is the possibility of getting a female shiny starter? This is what I did:

0.0122% of the 12.5% of females are shiny: 0.0122%*12.5% 0.000122*0.125 = 0.00001525 = 0.001525%.

Therefore it would take me about 100000 tries to get a female starter, which is so much more comparing to the 10000 tries to get any shiny starter.