**Given:** S_{1} and S_{2} are two swiches whose probabilities of working be given by

P(S_{1}) = \(\frac{4}{5}\) and P(S_{2}) = \(\frac{9}{10}\)

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

S_{1} and S_{2} 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(S_{1} ∩ S_{2}) = P(S_{1}) x P(S_{2})

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

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

**Therefore, **The probability that the current flows from terminal A to terminal B when S_{1 }and S_{2} are connected in series is \(\frac{18}{25}\)