Question

Martha types a 4−digit code into a keypad to unlock her car doors. The code uses the numbers 1 and 0. If the digits are selected at random, what is the probability of getting a code with exactly one 1? Enter your answer as a simplified fraction.

Answer 1

4 binary digits have 2^4 = 16 combinations.
The combinations with exactly one 1 are: 1000, 0100, 0010 and 0001. So 4 out of 16 codes have exactly one 1.

The chances of that are 4/16 = 1/4.