Question

A commuter uses a bus and a train to get to work. The train is more than 5 minutes late 1/6 of the times they use it The bus is more than 5 minutes late 3/5 of the times they use it. What is the probability that both the bus and train will be more than 5 minutes late?

Answer 1

Answer:

10% probability that both the bus and train will be more than 5 minutes late

Step-by-step explanation:

Independent events:

If two events, A and B, are independent, we have that:

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

What is the probability that both the bus and train will be more than 5 minutes late?

The bus being more than 5 minutes late is independent of the train, and vice versa. So

Event A: Bus more than 5 minutes late

Event B: Train more than 5 minutes late

The train is more than 5 minutes late 1/6 of the times they use it

This means that $P(B) = \frac{1}{6}$

The bus is more than 5 minutes late 3/5 of the times they use it.

This means that $P(A) = \frac{3}{5}$

Then

$P(A \cap B) = \frac{3}{5}*\frac{1}{6} = \frac{3}{30} = 0.1$

10% probability that both the bus and train will be more than 5 minutes late