Solution Found!
Consider the following portion of an electric circuit with
Chapter 2, Problem 97E(choose chapter or problem)
Consider the following portion of an electric circuit with three relays. Current will flow from
point a to point b if there is at least one closed path when the relays are activated. The relays
may malfunction and not close when activated. Suppose that the relays act independently of
one another and close properly when activated, with a probability of .9.
a What is the probability that current will flow when the relays are activated?
b Given that current flowed when the relays were activated, what is the probability that relay
1 functioned?
Questions & Answers
QUESTION:
Consider the following portion of an electric circuit with three relays. Current will flow from
point a to point b if there is at least one closed path when the relays are activated. The relays
may malfunction and not close when activated. Suppose that the relays act independently of
one another and close properly when activated, with a probability of .9.
a What is the probability that current will flow when the relays are activated?
b Given that current flowed when the relays were activated, what is the probability that relay
1 functioned?
ANSWER:
Answer:
Step 1 of 2:
(a)
In this question, we are asked to find the probability that current will flow when the relays are activated.
Consider the following portion of an electric circuit with three relays. Current will flow from point to point
if there is at least one closed path when the relays are activated.
Suppose that the relays work independently and close properly when activated, with a probability of .
Probability of the relay when closed (activated) = 0.9,
Hence,
=
,
…………….(1)
Since we have three relays in the circuit and all relays act independently of one another
So we can write,
Hence,
Hence the probability that current will flow when the relays are activated is 0.999.