Let S 1 and S 2 be two the switches and let their probabilities of working be given by P(S 1 ) = 2/3 and P(S 2 ) = 3/ 4 . Find the probability that the current flows from terminal A to terminal B, when S 1 and S 2 are installed in parallel, as shown below:

Question

Philoid · Accepted Answer

Given: S₁ and S₂ are two swiches whose probabilities of working be given by

P(S₁) = and P(S₂) =

To Find: the probability that the current flows from terminal A to terminal B when

S₁ and S₂ are connected in parallel.

Now, since current in parallel flows in two or more paths and hence the sum of currents through each path is equal to total current that flows from the source.

the flow of current from terminal A to terminal B in a parallel circuit is given by

P(S₁ S₂) = P(S₁) + P(S₂) - P(S₁ S₂)

= P(S₁) + P(S₂) –[ P(S₁) P(S₂)]

= + -

=

Therefore, The probability that the current flows from terminal A to terminal B when S₁ and S₂ are connected in parallel is

Let S1 and S2 be two the switches and let their probabilities of working be given by P(S1) = 2/3 and P(S2) = 3/4. Find the probability that the current flows from terminal A to terminal B, when S1 and S2 are installed in parallel, as shown below:

Let S₁ and S₂ be two the switches and let their probabilities of working be given by P(S₁) = 2/3 and P(S₂) = 3/₄. Find the probability that the current flows from terminal A to terminal B, when S₁ and S₂ are installed in parallel, as shown below: