Question

Outside a home, there is a 4-key keypad numbered 1 through 4. The correct 5-digit code will open the door. The numbers can be repeated in the code.
a) How many codes are possible?
b)Find the probability of entering the correct code on the first try?

Answer 1

a)There are 4 possible numbers (1,2,3,4) that can be placed in 5 places. Therefore the are

$$N = {4^5} = 1024$$

codes.

b)If we don't know the code (or it's part) we do it at 'full' random, so the probability is

$$p = {1 \over N} = {1 \over {1024}}$$