Question

What is the probability that the bulb is glowing for a circuit set up as:

|-------------(Bulb)-----------|
| |
| | (Voltage) |
| |
| |
|----(Switch-1)---(Switch-2)---|

Answer 1

probability that a switch is on = p, therefore probability that it is off = (1-p)
There are four possible configurations for the switches
1. A and B off [(1-p)(1-p)]
2. A and B on [ p * p ]
3. A on, B off [ p (1-p)]
4. B on, A off [ (1-p)p }
Only #2 leads to light.
so
p*2 = p^2
if p = 1/2
then 1/4