physics...........

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

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

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  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

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