Suppose an alarm clock has been set to ring after t hours, where t~exp(1/3). suppose further that your friend has been staring at the clock for exactly 7 hours and can confirm that it has not yet rung. at this point, your friend wants to know when the clock will finally ring. calculate for her the conditional probability that she will need to wait at least 3 more hours given she has already waited 7. next, calculate for her the conditional probability that she will need to wait at least x> 0 more hours given she has already waited 7.