Since there are 10 red marbles and 12 blue marbles, there are a total of 10 + 12, or 22 total marbles. This is important to keep in mind as we solve the different problems.
(a) There are 10 red marbles out of the 22 total marbles, so we have
10/22, which can be simplified by dividing both numerator and denominator by 2, which makes this 5/11.
(b) Every other marble is odd, regardless of color. For example, the red marbles are numbered
1 2 3 4 5 6 7 8 9 10, so the odd numbers are 1, 3, 5, 7, 9, for a total of 5 odd numbers.
The blue marbles are 1 2 3 4 5 6 7 8 9 10 11 12, so the odd numbers are 1, 3, 5, 7, 9, 11, for a total of 6 odd numbers.
5 + 6 = 11 odd marbles
Note: If you know there isn't anything strange about how the marbles are numbered, you can simply divide the total number of marbles by 2. There are quite a few different situations where it's not quite that simple: marbles numbered 1 to 11, marbles numbered every 4th number, etc, but we won't go into that now.
(c) We know there are a total of 10 red marbles, and a total of 11 odd marbles. However, we can't just add 10 and 11, as that would be 21, which is not quite right...
Some of the marbles are red AND odd, and we don't want to double count them. The few ways I can think of doing this problem:
* Count the red marbles, then count the blue marbles that are odd: 10 + 6 = 16
* Add the red marbles and odd marbles, then subtract the number of red marbles that are also odd, to get rid of duplicates: 10 + 11 - 5 = 16
(d) This problem is similar to part (c). Again, there are a couple ways of doing it. I will be using the method of counting blue marbles, then counting red marbles that are even.
12 + 5 = 17
