SOLUTION: a machine has 4 components;A,B,C and D for the mqachine to work,both A and D have tro work,and atleast one of B and C has to work.Probvability of A,B,c and D working are 0.8,0.8,0.

Algebra ->  Probability-and-statistics -> SOLUTION: a machine has 4 components;A,B,C and D for the mqachine to work,both A and D have tro work,and atleast one of B and C has to work.Probvability of A,B,c and D working are 0.8,0.8,0.      Log On


   

Question 981366: a machine has 4 components;A,B,C and D for the mqachine to work,both A and D have tro work,and atleast one of B and C has to work.Probvability of A,B,c and D working are 0.8,0.8,0.6 and 0.6 respectively.Assuming that components wok or fail indepedently of each other ,What is the probability that the machine works?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look at the possible working combinations
1.A working, D working, B working, C not working
2.A working, D working, C working, B not working
3.A working, D working, B working, C working
Those are the only possible combination for which the machine works.
Find the probability of each case by multiplying probabilities together.
P%5B1%5D=+0.8%280.6%29%280.8%29%280.4%29=0.1536
P%5B2%5D=+0.8%280.6%29%280.6%29%280.2%29=0.0576
P%5B3%5D=+0.8%280.6%29%280.8%29%280.6%29=0.2304
So then,
P=P%5B1%5D%2BP%5B2%5D%2BP%5B3%5D
P=0.1536%2B0.0576%2B0.2304
P=0.4416