To calculate the probability of picking a marble that is not red, we need to follow these steps:

1. Total number of marbles:
   The bag contains:

   • 5 blue marbles
   • 4 red marbles
   • 3 orange marbles

   The total number of marbles is: $5 + 4 + 3 = 12$

2. Number of marbles that are not red:
   The marbles that are not red are the blue and orange ones: $5 \, (\text{blue}) + 3 \, (\text{orange}) = 8$

3. Probability formula:
   The probability $P(\text{not red})$ is the number of favorable outcomes (not red) divided by the total number of outcomes (total marbles): $P(\text{not red}) = \frac{8}{12} = \frac{2}{3}$

Thus, the probability of picking a marble that is not red is $\frac{2}{3}$.

Would you like more details, or do you have any questions?

Here are 5 related questions to explore further:

1. What is the probability of picking a red marble?
2. If you pick two marbles without replacement, what is the probability that both are blue?
3. What is the probability of picking either a blue or an orange marble?
4. If one marble is picked, what is the probability that it is either red or orange?
5. If you add 2 more red marbles, how does the probability of not picking red change?

Tip: Probabilities can also be expressed as percentages by multiplying the fraction by 100.