Final answer:
To find the odds in favor of drawing a blue marble, we calculate the ratio of the number of blue marbles (42) to the number of non-blue marbles (126), which simplifies to 1 to 3, making the correct answer B.1 to 3.
Step-by-step explanation:
The question requires us to calculate the odds in favor of drawing a blue marble from a box containing a total of 168 marbles of various colors. To find the odds in favor of an event, we use the ratio of the number of successful outcomes to the number of unsuccessful outcomes. In this case, the successful outcome is drawing a blue marble, and there are 42 blue marbles out of 168 total marbles.
First, we find the total number of unsuccessful outcomes by subtracting the number of blue marbles from the total number of marbles: 168 total marbles - 42 blue marbles = 126 non-blue marbles.
The odds in favor of drawing a blue marble are the ratio of the number of blue marbles to the number of non-blue marbles, which is 42 to 126. This ratio can be simplified by dividing both numbers by their greatest common divisor, which is 42, resulting in 1 to 3. Therefore, the odds in favor of drawing a blue marble is 1 to 3.