# statistics

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Suppose that each unit of a system is up with probability 2/3 and down with probability 1/3. Different units are independent. For each one of the systems shown below, calculate the probability that the whole system is up (that is, that there exists a path from the left end to the right end, consisting entirely of units that are up).

What is the probability that the following system is up?

What is the probability that the following system is up?

• statistics - ,

if n units are independent and the probability of each being up is 2/3 then the probability of all n being up is (2/3)^n
HOWEVER I can not see your flow chart and therefore can not evaluate parallel paths
if there are two ways to get from A to B
and the probability of failure of each branch is 1/3
then the probability of both failing is (1/3)(1/3) = 1/9 and the probability of getting from A to B one way or another is 1 - 1/9 = 8/9

• statistics - ,

With f the probability of fail

a) First branch: f1=(1/3)*(1/3)
Second branch: f2=1/3

Thus:
The probability of success of the system is:(1-(1/3)*(1/3))*2/3
=2/3*(1-1/9)=(2*8)/(3*9)

b)
First branch:
f1= 1-(2/3)*(2/3)=5/9
second branch
f2=1/3

Thus:
The probability of success of the system is: 1-(5/9)*(1/3)

• statistics - ,

a)diagrams
-p1 -(p2)- end
-(p3)- end

b)-(p1)-(p2)- end
-(p3)----- end