Question

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 0.26. The probability that Napoleon and Pedro catch the bus is 0.25. However, the probability that they make it to their first period class on time, given that they catch the bus is 0.61. What is the probability that Napoleon and Pedro catch the bus and make it to their first period class on time

Answer 1

Answer:

15.25% probability that Napoleon and Pedro catch the bus and make it to their first period class on time

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this problem, we have that:

Event A: Both Napoleon and Pedro catch the bus, so P(A) = 0.25.

Event B: Making to their first period class on time.

However, the probability that they make it to their first period class on time, given that they catch the bus is 0.61.

This means that $P(B|A) = 0.61$

What is the probability that Napoleon and Pedro catch the bus and make it to their first period class on time

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

$0.61 = \frac{P(A \cap B)}{0.25}$

$P(A \cap B) = 0.61*0.25$

$P(A \cap B) = 0.1525$

15.25% probability that Napoleon and Pedro catch the bus and make it to their first period class on time