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