06-06-2003, 03:46 AM
Usually to find the max or min you pick end cases and special cases when you know any case in between is in the middle. A few choices to calculate along with the solution could be:
50 balls in each, one color per jar
50 balls in each, equal number of colors per jar
99 balls in one, white ball in the other
99 balls in one, black ball in the other
It is easy to see from this that the answer is what you have already said. You can then pick some arbitray combonation in between these cases, such as 50 balls in each, 75% white in one jar, 25% white in the other jar and you will see the probabilty lies between the min and max you have calculated for the special cases.
50 balls in each, one color per jar
50 balls in each, equal number of colors per jar
99 balls in one, white ball in the other
99 balls in one, black ball in the other
It is easy to see from this that the answer is what you have already said. You can then pick some arbitray combonation in between these cases, such as 50 balls in each, 75% white in one jar, 25% white in the other jar and you will see the probabilty lies between the min and max you have calculated for the special cases.