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?

The probability that the machine works in the morning is 50%.  This means that out of 100 times it works, it will not overheat 50 times.

The probability that the overheats late if it worked  in the morning is 15%. this means that 15% our of the 50 times in the morning when it worked will satisfy this condition, which is 7.5 - so if the machine runs 100 times, it will overheat only in the evening 7.5 times.
 
The probability that it will overheat only in the evening is 7.5%!