Final answer:
In the context of marbles in a bag, we found there were 7 white marbles before the game, 16 marbles were chosen for the game, and we cannot definitively calculate how many white marbles were not chosen without further information.
Step-by-step explanation:
The question involves solving problems related to probability and combinatorics within a given context of marbles in a bag. This situation typically falls under basic probability, which is a part of middle school or early high school mathematics.
(a) Since there are 24 marbles in total and 17 are black, the number of white marbles in the bag before the game can be calculated by subtracting 17 from 24, giving us 7 white marbles. To determine how many of the bag's white marbles were not chosen, we must first find out how many marbles were chosen for the game, which is 2/3 of the total marbles. Multiplying 24 by 2/3 gives us 16. Since the selection does not specify color, we cannot definitively calculate how many white marbles were not chosen without additional information.
(b) To find how many marbles were chosen, we use the fraction 2/3 as mentioned in the question: 2/3 of 24 marbles equals 16. This means 16 marbles were chosen for the game.
(c) We answered this in part (a): there were 7 white marbles in the bag before the game.