Minor correction: in a few billion years our sun will expand into its red giant death phase.
Also: our star can’t go nova by our understanding of astrophysics. If it actually can, then we might need to throw out a lot of astrophysics, including predictions on when our star will expand.
Also also: the odds of the dice giving double 6s is MUCH higher than our sun going nova at any point in time even if it could go nova and was overdue.
That last part is what the Bayesian scientist is wagering on, it’s not missing, as op suggested
Ah, gotcha. I tried learning Bayesian probability once and failed utterly. One of the only classes I just barely passed (stat was the other). My brain just barely computes it.
The intuition is exactly your argument:
When the machine says yes it’s either because
(1) the sun went nova (vanishingly small chance) and machine rolled truth (prob 35/36) – the joint probability of this (the product) is near zero
OR
(2) sun didn’t go nova (prob of basically one) and machine rolled lie (prob 1/36) – joint prob near 1/36
Think of joint probability as the total likelihood. It is much more likely we are in scenario 2 because the total likelihood of that event (just under 1/36) is astronomically higher than the alternative (near zero)
I’m skipping stuff but hopefully my words make clear what they math doesn’t always
