Question

In a factory, the chance that a certain machine works without overheating in the morning is 50%. If it runs smoothly all morning, then there is an 85% chance that it will continue for the rest of the day and a 15% chance that it will stop due to overheating. What is the probability that on a given day it will work in the morning and overheat later on?

Answer 1

7.5%.

So, the probability that on a given day it will work in the morning is 50% and the probability that it won't is 50%.

If it works in the morning, we're at 50%. Then, it has a 15% chance of failure.
So, it is 50 times 50%, or 7.5%.