Now that I see this problem again, my thoughts on it are slightly different.
In the version with no bombs, there’s a possible scenario where the picker draws a red ball but lies to you by keeping silent. So, there’s a viable way for “you hear nothing” AND “Jar R” to happen.
But in the version with bombs, the scenario with “you are alive” AND “Jar R” can never happen. So, being alive in the with-bomb version is stronger evidence for Jar S than hearing nothing in the no-bomb version.
Okay, sure. The picker could be lying or speaking quietly; the bomb could be malfunctioning or have a timer that hasn’t gone off yet. (Note to self: put down the ball as soon as you find out that it could be a bomb.) These things don’t seem like they should be the point of a thought experiment.
Before I actually do the math, “you hear nothing” appears to affect my estimate exactly in the same way as “you’re still alive.”
This seems like the obvious answer to me as well. What am I missing?
Now that I see this problem again, my thoughts on it are slightly different.
In the version with no bombs, there’s a possible scenario where the picker draws a red ball but lies to you by keeping silent. So, there’s a viable way for “you hear nothing” AND “Jar R” to happen.
But in the version with bombs, the scenario with “you are alive” AND “Jar R” can never happen. So, being alive in the with-bomb version is stronger evidence for Jar S than hearing nothing in the no-bomb version.
Okay, sure. The picker could be lying or speaking quietly; the bomb could be malfunctioning or have a timer that hasn’t gone off yet. (Note to self: put down the ball as soon as you find out that it could be a bomb.) These things don’t seem like they should be the point of a thought experiment.