some numbers into it probability of a measurement Z given the doors open is 0.6 Zija the door is not open is 0.3 so we see that when the door is open we are more likely to measure Z as the outcome than when the door is not open so if we measure Z which should increase our probability that the door is open and our prior is 50% well we can apply Bayes rule we measured Z we can look at Bayes rule fill this in do the math which is described to find indeed that now after measuring Z which favors the door being open we have more specifically 0.67