probability that the door is open now you could have another measurement imagine of another sensor wait wait go yeah let matching we have another sensor z2 how can we integrate that well we can again apply Bayes rule we already know that we can apply Bayes rule again even with conditioning in the back we already conditioned on one measurement just in a condition on the next measurement we actually do this as many times as we want so the condition on many measurements we can do it one at a time and build it up so here we have the