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

"probability that on a given day it will work in the morning and overheat later on"

we can split this into two probabilities:

(probability that it will work in the morning) * (probability that it will overheat, given that it ran all morning)

both of these probabilities are mentioned in the problem so you just have to take the appropriate #'s from the problem and multiply.