00:01
All right, so for this problem, in part a, we have that the probability of the clock failing on an exam, or on the day of an important exam, is going to be the same as the probability of the clock failing on any other day.
00:13
So if it fails 16 .1 % of the time, that means that the probability of it failing on the day of an exam would be 0 .161.
00:22
Then, for part b, where we're asked the probability of both clocks failing, if he is using two such alarm clocks, we would find that probability by taking the probability that one of them fails, times the probability that the second one also fails.
00:44
So we'd have 0 .161 to the power of 2, which means that just by having one redundancy, having two clocks instead of 1, this reduces the chance of both clocks failing, and therefore the student not being woken up in time for the exam, that reduces the probability to 0 .0266.
01:04
And then if we have three independent alarm clocks, the probability that three of them fail, or all three fail, that would be 0 .161 to the power of three, which gives a probability of roughly 0 .0 .004.
01:21
And then for part d, we're asked, do the second and third alarm clocks result in greatly improved reliability? clearly, the answer is yes...