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Let S1 and S2 be the two switches and let their probabilities of working be given by P(S1) = 4/5 and P(S2) = 9/10. 

Find the probability that the current flows from the terminal A to terminal B when S1 and S2 are installed in series, shown as follows:

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

P(S1) = \(\frac{4}{5}\) and P(S2) = \(\frac{9}{10}\)

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

S1 and S2 are connected in series.

Now, since the current in series flows from end to end

\(\Rightarrow\) the flow of current from terminal A to terminal B is given by

P(S1 ∩ S2) = P(S1) x P(S2)

\(\frac{4}{5}\times\frac{9}{10}\)

\(\frac{18}{25}\)

Therefore, The probability that the current flows from terminal A to terminal B when S1 and S2 are connected in series is \(\frac{18}{25}\)

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