Your friend Janaiah has an active iPhone. Her phone rings with probability 1/2 each minute when it is on. (For purposes of making this a clean model, let's imagine that once each minute, an invisible fair coin is being flipped somewhere, and if it comes up "heads," then Janaiah's phone will ring that minute. These flips are independent, so if her phone is on, the probability that it does not ring for n consecutive minutes is (1/2)n .) Also, at any given point in time, in the absence of any other information,there's a 98% probability that her phone is on. You're sitting with Janaiah the next day and you notice that her phone isn't ringing. You begin to wonder how many consecutive minutes of phone silence it would take, starting from when you first sit down with her, before the probability that her phone is off first exceeded 50%. Give the smallest whole number with this property i.e. the smallest whole number 1 n so that after n consecutive minutes of phone silence, the probability that her phone is off is greater than 50%. Give an explanation for your answer using Bayes' Rule. (Her phone has either been on the whole time you're sitting with her or off the whole time you're sitting with her.)