To find the probability that both marbles chosen are red, let's follow these steps:

1. Total marbles in the jar:
   There are 13 red marbles and 23 blue marbles, so the total number of marbles is:
   $13 + 23 = 36$

2. Probability of drawing the first red marble:
   The probability of drawing one red marble on the first draw is:
   $\frac{13}{36}$

3. Probability of drawing the second red marble (after drawing the first red):
   Once the first red marble is drawn, there are 12 red marbles left and only 35 marbles total left in the jar:
   $\frac{12}{35}$

4. Combined probability for both events:
   To find the probability that both marbles are red, multiply the probabilities of the two independent events:
   $\frac{13}{36} \times \frac{12}{35} = \frac{156}{1260}$

5. Simplify and round to four decimal places:
   Simplifying the fraction gives:
   $\frac{156}{1260} = \frac{13}{105} \approx 0.1238$

Therefore, the probability that both marbles chosen are red is approximately 0.1238.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. What is the probability of drawing two blue marbles in a row?
2. How does the probability change if we add more marbles of a different color?
3. What is the probability of drawing one red and one blue marble?
4. How would the probability change if the marbles were drawn one at a time with replacement?
5. How can this problem be represented and solved using combinations?

Tip: When calculating probabilities for sequential events, always adjust the total count for each subsequent event based on prior outcomes.