A lock has two buttons: a "0" button and a "1" button. To open a door you need to push the buttons according to a preset 8-bit sequence. How many sequences are there? Suppose you press an arbitrary 8-bit sequence; what is the probability that the door opens? If the first try does not succeed in opening the door, you try another number; what is the probability of success?

Step-by-step explanation:

The problem relates to filling 8 vacant positions by either 0 or 1

each position can be filled by 2 ways so no of permutation

= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

= 256

b)

Probability of opening of lock in first arbitrary attempt

= 1 / 256

c) If first fails, there are remaining 255 permutations, so

probability of opening the lock in second arbitrary attempt

= 1 / 255.