Suppose a jar contains 13 red marbles and 23 blue marbles. If 2 marbles are randomly chosen from the jar at the same time, find the probability that both marbles are red. Round your answer to four decimal places.

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.

Find the probability of drawing two red marbles from a jar containing 13 red and 23 blue marbles. Learn how to use the multiplication rule of probability for dependent events with step-by-step explanations. Suitable for Grades 8-10.

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