An electronic device produces an output of 0, 1 or 3 volts, each time it is operated, with probabilities 1/2, 1/3 and 1/6 respectively. The random variable X denotes the
result of adding the outputs for two such devices which act independently find probability

(a) Note the probability distribution of X.
(b) In 360 independent operations of the device, state on how many occasions you
would expect the output to be 1 volt.
(c) What is the expected output?

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?