WILL GIVE A LOT OF POINTS A man has 100 light switches in his house which are numbered from 1 to 100. One night he goes through every switch and turns it on. Then he goes around a second time and turns every other switch (2,4,6,8) off. Then he goes around a third time and turns every third switch off if it is on and on if it is off. Then he goes around and flips every foruth switch and so on. How many lights are left on after the 100th time?

Assume that there is a 11% rate of disk drive failure in a year. a. if all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. if copies of all your computer data are stored on four independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?