Question

Probability of the closing of each relay of the circuit shown below is given by p. If all the

relays function independently, what is the probability that a circuit exists between the terminals L

and R?
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Answer 1

Step-by-step explanation:

The probability of the closing of each switch in the circuit shown above is given by p. If all switches function independently, what is the probability that a current exists between the terminals

Answer 2

Given: closing of each relay of the circuit shown below is given by p

To Find: the probability that a circuit exists between the terminals L

Solution:

To determine the probability that a circuit exists between the terminals L and R, we can use the concept of the complement of an event. That is, we can calculate the probability that there is no circuit between L and R and then subtract this probability from 1 to get the desired probability.

Consider the path from L to R through the top relay. The open probability is p and the closed probability is (1-p). Ans same the bottom open probability is p and the bottom closed probability is (1-p).

For there to be no circuit between L and R, both paths must be closed. The probability of this happening is (1-p)^2 since the paths function independently. Therefore, the probability of a circuit existing between L and R is:

P(circuit exists) = 1 - P(no circuit exists)

= 1 - (1-p)^2

= 2p - p^2

So the probability of a circuit existing between L and R is 2p - p^2.

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