Question

If two switches S1 and S2 have respectively 90% and 80% chances of working, then the value of 100 X probability that the circuit will work = ___

Answer 1

This is a situation where we apply the concept of independent events. That is for two independent events A and B, $P(A\cap B)=P\left(A\right)P\left(B\right)$.
So, what are the events that we are considering here?
For that let us consider the event, whose probability has to be calculated, given circuit works. Circuit will work when both the switches work. Shouldn't we consider the probabilities that the lamp works and the battery works? Since they are not given in question, we will assume everything else works(or is in ideal situation)
So the question about ‘circuit works’ can be split into switch one works and switch two works. Are these two events independent ? Yes, because switch one works does not depend on if switch 2 works (Here also, we consider only the information given in the question)
Let A be the event S1 works and B be the event S2 works.
P(circuit works) = P(S1 and S2 works)
$=P(A\cap B)$
$=P\left(A\right).P\left(B\right)$
$=\frac{90}{100}\frac{80}{100}$
$=0.72$
$\Rightarrow 100P\left(circuitworks\right)=72$