To find the probability of picking a blue marble from the bag, we first need to determine the total number of marbles.
The total number of marbles is calculated as follows:
- Blue marbles: 8
- Red marbles: 24
- Green marbles: 16
- Yellow marbles: 4
Now, adding these quantities together:
\[ \text{Total marbles} = 8 + 24 + 16 + 4 = 52 \]
Now that we have the total number of marbles, we can calculate the probability of picking a blue marble. The probability \( P \) of an event is given by the formula:
\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
In this case, the number of favorable outcomes (picking a blue marble) is 8, and the total number of outcomes (total marbles) is 52.
Thus, the probability of picking a blue marble is:
\[ P(\text{blue}) = \frac{8}{52} = \frac{2}{13} \]
So, the probability of picking a blue marble at random out of the bag is \( \frac{2}{13} \).