Question

Outside a​ home, there is aa 44​-key keypad numbered 11 through 44. The correct sixsix​-digit code will open the garage door. The numbers can be repeated in the code.

​(a) How many codes are​ possible? ​
(b) What is the probability of entering the correct code on the first​ try, assuming that the owner​ doesn't remember the​ code?

Answer 1

a) 4,096

b) 0.000244

Explanation:

a)

By the Fundamental rule of counting, there are

4*4*4*4*4*4 = 4,096

ways of forming six-digit arrangements where each position has 4 possibilities (1 to 4)

b)

The probability of entering the correct code on the first try, assuming that the owner does not remember the code is

1/4096 = 0.000244