cynara has a bag of red, blue, and black pens. She randomly selects a pen, records the color, and puts it back in the bag, She does this a total of 30 times and selects 6 red pens, 10 blue pens, and 14 black pens. Based on this information, what is the probability that Cynara will select a blue pen, return it to the bag, and then select a red pen?

To find the probability that Cynara will select a blue pen and then a red pen, we first need to determine the probabilities of selecting each color based on her experiment.

Cynara selected pens in total:
- Red pens: 6
- Blue pens: 10
- Black pens: 14

Total selections = 6 + 10 + 14 = 30.

Now, we can calculate the probabilities for each color:

1. Probability of selecting a Blue pen (P(Blue)):
\[
P(\text{Blue}) = \frac{\text{Number of Blue pens}}{\text{Total Pens}} = \frac{10}{30} = \frac{1}{3}.
\]

2. Probability of selecting a Red pen (P(Red)):
\[
P(\text{Red}) = \frac{\text{Number of Red pens}}{\text{Total Pens}} = \frac{6}{30} = \frac{1}{5}.
\]

Now, since the selections are done with replacement, the two events (selecting a blue pen and then selecting a red pen) are independent. Therefore, we can calculate the joint probability of these two events occurring one after the other by multiplying their probabilities:

\[
P(\text{Blue then Red}) = P(\text{Blue}) \times P(\text{Red}) = \left(\frac{1}{3}\right) \times \left(\frac{1}{5}\right) = \frac{1}{15}.
\]

Thus, the probability that Cynara will select a blue pen, return it to the bag, and then select a red pen is:

\[
\boxed{\frac{1}{15}}.
\]