Hey there! I'm happy to help!
We see now that there is a 50% chance of the taxi driver picking the poisonous pill each time. This seems like a high chance at first, but if you keep on doing it over and over again the probability is smaller and smaller that he will survive. The first time it is 50%, then 25%, then 12.5%, and it gets smaller and smaller. Therefore, there must be something else going on for this taxi driver to have such good luck.
We see that passenger is the one who picks it because if the taxi driver picked it, it would be rigged. However, there has to be a way that the passenger always dies. Therefore, it makes the most sense that the poison isn't actually in the pills, but in something else.
We see that each passenger had to swallow the pill with water. When they say that one of them is harmless and the other one is poisonous, they did not clarify that they were talking about the pills. They could have easily been talking about the glasses of water. And, the passenger does not pick which glass of water to drink, so it could easily be rigged so that they are drinking poisoned water.
Sherlock could have easily asked to swallow the pill with his own water, another drink, or to swallow it without any liquid.
I hope that this helps! Have a wonderful day!
