A pass code is created by combining one-digit prime numbers. What is t

There are 4 one digit prime numbers - 2,3,5,7.

The total number of 4 digit numbers possible is 4*4*4*4(since digits can be repeated)
In order to determine how many of these 4 digit numbers are divisible by 12,
we employ the following method :
For a number to be divisible by 12, it has to be divisible by both 3 and 4.

Only numbers ending with 32,52 and 72 can be divisible by 4
as the rule for divisibility of 4 is that the last 2 digits must be divisible by 4.
For the number to be divisible by 3, the sum of the digits must add to give a multiple of 3 :

We have the possible total combinations for the numbers ending :

1. _ _ 32 are 2532,5232,5532,3732,7332, and2232(6 combinations)
2. _ _ 52 are 7752,3552,5352,2352, and 3252(5 combinations)
3. _ _ 72 are 5772,7572,2772,7272, and 3372(5 combinations)

P(Numbers divisible by 12) = P(A) = 6+5+5 = 16
Also P(T) = P(Total possible combinations) = 256

The probability is \(\frac{P(A)}{P(T)}\) = \(\frac{16}{256} = \frac{1}{16}\) (Option A)