Here is the question If the backup computer must be activate

Here is the question:

If the backup computer must be activated by a switch in the event that the first computer fails, and the switch has a reliability of .95, what is the overall reliability of the system? (Both the switch and the backup computer must function in order for the backup to take over.)

Here are the previous questions that I do have answers to:

The first being:

The guidance system of a ship is controlled by a computer that has three major modules. In order for the computer to function properly, all three modules must function. Two of the modules have reliabilities of .90, and the other has a reliability of .93.

What is the reliability of the computer? (Round your answer to 4 decimal places.) My answer to this one was 0.7533

The second question was :

A backup computer identical to the one being used will be installed to improve overall reliability. Assuming the new computer automatically functions if the main one fails, determine the resulting reliability

My answer was 0.9391

Solution

1) Reliability = . 0.90*0.90*0.93 = 0.7533

2). Failure rate in the first case is (1-reliability)= 1-0.7533 = 0.2467,

    2nd will function for 0.2467*0.7533 = 0.1858, resulting gap is (0.2467-0.1858) = 0.0609,

    Hence reliability is (1- 0.0609) = 0.9391

3). Reliability of switch is 0.95. Since both switch and computer should function,

     Switch and 2nd comp work in 0.2467*0.7533*0.95 = 0.1765,

      Resulting gap is (0.2467-0.1765) = 0.0701,

       Hence reliability is (1- 0.0701) = 0.9298