Person A chooses an integer between 1 and 100 at random, then B can guess that number in (at most) 7 attempts, i.e. $\log_2(100)+1=7$. What if now A chooses an integer from a distribution that is known to B (B knows the probability of each number being selected but does not know the number). Can B use this extra information to guess that number in fewer attempts? What would be the best strategy here?