Question 1197738
**1. Define Events**

* Let **A** be the event that Napoleon and Pedro make it to their first period class on time.
* Let **B** be the event that Napoleon and Pedro catch the bus.

**2. Given Probabilities**

* P(A) = 0.27 
* P(B) = 0.50
* P(A|B) = 0.81 (Probability of making it to class on time given they catch the bus)

**3. Find the Probability of Catching the Bus and Making it to Class on Time (P(A ∩ B))**

* We can use the conditional probability formula:
    * P(A|B) = P(A ∩ B) / P(B)

* Rearrange to solve for P(A ∩ B):
    * P(A ∩ B) = P(A|B) * P(B)

* Substitute the given values:
    * P(A ∩ B) = 0.81 * 0.50 
    * P(A ∩ B) = 0.4050

**Therefore, the probability that Napoleon and Pedro catch the bus and make it to their first period class on time is 0.4050.**