Question

A bulb can either be on or off. A board contains connected to a randomization circuit that lights up a random sequence every time it is turned on. What is the probability that all the lights will switch on

Answer 1

The question is incomplete. The complete question is :

A bulb can either be on or off. A board contains 20 bulbs connected to a randomization circuit that lights up a random sequence every time it is turned on. What is the probability that all the lights will switch on ?

Solution :

It is given that :

There is board connected to = 20 bulbs

And one can either be put ON or put OFF.

Therefore the chance that a bulb is ON = $\frac{1}{2}$

It is given that every time a bulb turns ON, the board lights up in a random sequence.

Therefore, the probability of all the lights to be switched ON is given by :

$=\left(\frac{1}{2}\right)^{20}$

$=\frac{(1)^{20}}{(2)^{20}}$

$=\frac{1}{1048576}$