Question 2 4 pts A company owns a machine made of 4 differen

Question 2 (4 pts) A company owns a machine made of 4 different devices (d1, d2, d3, d4). Each of these devices could fail at any time which causes the machine failure. Devices fail 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? 3- A failure has happen, what is the probability the machine can be repaired? Bonus Question (3pts): 5-What is the probability that the machine can be repaired after two consecutive failures?

Solution

1) machine can be fail if any of one device fail this means there are cases when machine can fail

case 1: when one devie fail

total ways = 4P1 = 4ways

case 2: when two device fail

ways = 4P2 = 12 WAYS

CASE 3: WHEN 3 DEVICE FAIL

WAYS = 4P3= 4 WAYS

CASE 4 : WHEN 4 DEVICE FAIL

WAYS = 4P4= 1

TOTAL WAYS = 12+4+12+1= 29 WAYS