All bags have the same number of oranges, but they do not weigh the same. You would not like to be cheated, or in other words, to not buy a bag below the median weight.
You begin by grabbing a bag with each hand to compare them. Once you decide on the heavier one you discard the one that feels lighter, keeping the one that feels heavier in your other hand, and pick up another bag with your free hand to make another comparison and continue the process.
Given that you are right about which bag is heavier 90% of the time (for simplicity assume your chances of misjudging the heavier of two bags are independent of their weight difference). How many bags will you have to pick up to be 85% certain that you are not being cheated?.
The number of bags to choose from is very large and there are no bags whose weight is equal to the median weight.
