A five digit number if formed by writing the digits 1, 2,3,4,5 in a random order without repetitions. Then, the probability that the number is divisible by 4 is

$\frac{1}{5}$

Total number of five digit numbers formed by the digits 1, 2, 3, 4, 5 is 51. A five digit number formed by the digits 1,2,3,4,5 will be divisible by 4 if the number formed by the last two digits is divisible by 4. Last two digits can be 12, 24, 32, 52.

Corresponding each of these are 3! arrangements of the remaining three digits.

∴ Total number of five digit numbers divisible by 4 is (3! × 4)

Hence, required probability $=\frac{3! × 4}{5!}=\frac{1}{5}$