Question

If the switches at 2, 3, 4, and 5 are independently closed or open with probabilities 0.1 (for closed) and 0.9 (for open), what is the probability of a closed path between the input line on the left and the output line on the right

Answer 1

Complete Question

The Complete Question is attached below

Answer:

$P(X)=0.0163$

Step-by-step explanation:

From the question we are told that

Probability of open $P(x)O=0.9$

Probability of open $P(x)C=0.1$

Generally the equation for Probability of a closed path between the input line on the left and the output line on the right is  mathematically given by

 $P(X)=(P(3\&5)C*P(2\&4)C)+(P(2\&4)O+P(2\&4)C*P(1\&3)O)+(P(1\&3)C-P(3\&5)C*P(2\&4)C)$

 $P(X)= 0.1*0.1*(0.1*0.1+0.9*0.9 ) + 0.1*0.1*(0.9*0.9 + 0.1*0.1) - 0.1*0.1*0.1*0.1$

 $P(X)=0.0163$