Chinese, English, & Probabilities

I just discovered a Chinese-learning blog that looked very interesting. I read a few entries, and came up across a post about some phonetic coincidences between English words and their Chinese translation.

This is a very interesting topic, as it has some kind of mystical appeal. However, every time someone wonders whether something is just a coincidence or not, I have a strong urge to work out the math behind it, and find out exactly what the odds are. So I have done a bit of number crunching. Here goes:

According to this table: Wikipedia Pinyin Table Chinese words have a possibility of 402 different sounds (I counted). That's not including the intonations, since I'm assuming that "fee" (in English), for instance, would be deemed similar to "fei" whether it's the 1st tone or the 4th. This means that any Chinese word would have to match one of these 402 sounds.

Assuming that every english word has a corresponding chinese word, and that every english sound has a corresponding sound in Chinese that can be deemed "close enough", it means that given a random English word, and a random Chinese sound, there are 1 in 402 chances that the meaning of a chinese word matching that sound corresponds to the same definition in English.

Therefore, for every English word, there is a 1/402 chance that its Chinese equivalent has the same sound. (assuming every Chinese sound can correspond to an English one. )

If we then assume (conservative estimate) that there are 3500 single-syllable words in English (Dr. Phyllis Fisher's word list) and every word having a 1 in 402 chance of finding its correspondent in Chinese, then the odds would be that 3500 X 1/402 = 8.7 English words would sound similar in chinese.

The odds would be even more favourable if you decide that sounds like zh/z, ch/c, sh/s, an/en, ang/eng ai/ei, etc. are similar enough to be considered identical, and if you assume there are more one-syllable English words.