SOLUTION: Based on a study from the Chronicles of Flippin'' Awesomeness, the probability that Napoleon and Pedro make it to their first period class on time is 0.27. The probability that Na

Question 1197738: Based on a study from the Chronicles of Flippin'' Awesomeness, the probability that Napoleon and Pedro make it to their first period class on time is 0.27. The probability that Napoleon and Pedro catch the bus is 0.50. However, the probability that they make it to their first period class on time, given that they catch the bus is 0.81. What is the probability that Napoleon and Pedro catch the bus and make it to their first period class on time?
Answer in decimal form. Round to 4 decimal places as needed.

Answer by onyulee(41) (Show Source): You can put this solution on YOUR website!
**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.**

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