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

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%!