Final answer:
The probability of removing the brown ball when 17 balls are removed from a bag containing 18 balls is 1 out of 18.
Step-by-step explanation:
The probability of removing the brown ball when 17 balls are removed from the bag at random is determined by considering the total outcomes and the favorable outcomes.
Since there is only one brown ball, the favorable outcomes are just the scenarios in which the brown ball is one of the balls removed.
Given that the total balls are 18, when you remove 17 balls, the chances of the one remaining ball (the one not removed) being the brown ball is the same as the chances of removing the brown ball in the 17 selected (since by symmetry, any ball is equally likely to be the left-out ball). Thus the probability is 1 out of 18, since there are 18 equally likely balls that could remain.