I think that you're assuming that the lawyers calculate something like expected utility before asking the question and then correct their expected value once they have information when it's more likely that they just start off with some generic starting point about how the juror is likely to vote and then use demographic information to pin down a better estimate.

Let's say that my employer pays me x amount per period and I think I may have gotten a raise to amount x+y. You're suggesting that I would go through the process of calculating my "expected" salary by taking (p-1)x+p(x+y) (where p is my estimation of the probability of getting the raise). Of course if I do this and then ask my boss whether I got the raise I will revise my expected salary upwards if I get an affirmative answer and downwards if I get a negative answer, but the calculating the "expected salary" first doesn't offer any benefit over just going and asking and then figuring out what my salary will be (as the two methods should provide the same final answer anyways) and so in this case I only revise my expectation upwards with a positive and downwards with a negative.