# 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.

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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:

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

P(S1) = $\frac{2}{3}$ and P(S2) = $\frac{3}{4}$

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.

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

$\frac{11}{12}$

Therefore, The probability that the current flows from terminal A to terminal B when S1 and S2 are connected in parallel is$\frac{11}{12}$