I just finished watching a film where the characters had estimated a fatality rate of $60-70\%$, say.
Does this make sense? They are saying that the probability of death is between $60$ and $70\%$ but then surely what they actually mean is that the probability is, at its best estimate, something like $65\%$ and the range is meaningless.
I understand that one could take $2$ biased coins, each having a probability of heads of $60$ and $70\%$ respectively but taking a coin at random and flipping it would give, by Bayes', a $65\%$ chance of a heads.
I would like to know if, $1.$ This probability range makes sense in this context and $2.$ An $\mathit{estimated}$ probability range can make sense in any context.
It makes perfect sense in the real world, where the numerical values of most probabilities are not known with perfect accuracy. Suppose in your movie the quoted chances were for a patient surviving some risky operation. If that particular operation had only been performed 360 times before, ever, and 234 patients survived, one would not know the exact survival probability for the operation, and a standard recipe for calculating "confidence intervals" for that probability might give a range such as the one you quoted. Even then the prediction would be understood to be even more inexact, as (for instance) the patient in question might be different from the previous patients, and the doctors involved might have honed their skills since they first started doing the operation.