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?

Let's imagine that we turn the machine on 100 times. (this will make the percent conversion easier)

the chance that works in the morning is 50%  of 100 so it will work 50 times.

the chance that it will then continue for the rest of the day is 15% so 15%*50 (the number of times it worked), which is 7.5 times.

our times actually represented percent, so the answer is : 7.5%!