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? 4%

Answer 1

It has to go through two steps,
first: works in the morning at 50% 
second : overheats rest of the day at 15%
Probability that it will work in the morning and overheats rest of the day is the product of the two probabilities, namely
Probability=0.50*0.15=0.075, or 7.5%.