A company owns a machine made of 4 different devices d1 d2 d

A company owns a machine made of 4 different devices (d1, d2, d3, d4) Each of these devices could fad at any time winch rouses the machine failure. Devices ail independently. The company is keeping only one spare replacement of each of the 4 devices so that in case of failure, the machine can be repaired by changing the defective devices 1-How many failure scenarios are possible? (In how many ways the machine can fail?) 2-A failure has happen, what is the probability that this failure is caused by only one device? A failure has happen, what is the probability the machine can be repaired\'? 5-What is the probability that the machine can be repaired after two consecutive failures?

Solution

1. the possible number of failure scenarios are 4! = 24

2. Probability that the failure is caused only by one machine = 1/4 =0.25

3. Probability that the machine is repaired = 1/4 =0.25

5. probability that the machine can be repaired after two consecutive failures = 1/4*1/4 = 0.25*0.25 = 0.0625