NL-NWO 1984 Problem 2

The circuit diagram drawn (see figure ) contains a battery $B$ , a lamp $L$ and five switches $S_1$ to $S_5$ . The probability that switch $S_3$ is closed (makes contact) is $\frac23$ , for the other four switches that probability is $\frac12$ (the probabilities are mutually independent). Calculate the probability that the light is on.