Let's first determine the total number of marbles Danielle has in her bag. She has 5 red marbles, 8 yellow marbles, 3 blue marbles, and 1 green marble. So in total, she has 5 + 8 + 3 + 1 = 17 marbles.
Now, let's figure out the number of marbles that meet Danielle's criteria of being either red or blue. She has 5 red marbles and 3 blue marbles, which together make 5 + 3 = 8 marbles.
The probability of an event is calculated as the ratio of the favorable outcomes to the total possible outcomes.
Here, the favorable outcome is picking a red or a blue marble, and the total possible outcomes is the total number of all marbles in the bag.
Therefore, the probability of picking a red or blue marble is 8 (red and blue marbles) divided by 17 (total marbles).
As a result, the probability is around 0.47058823529411764 when calculated in a decimal format. If you prefer to leave your answer as a fraction, this would roughly be equivalent to 8/17.
So, Danielle has a 8 in 17 or approximately a 0.47 chance (rounded to two decimal places) to draw a either a red or blue marble from the bag.