If a three-digit number is chosen at random, what is the probability that it is divisible neither by 3 nor by 4?

There are total 900, 3-digit numbers.

So, number of 3-digit numbers, divisible by 3 =$$\left[\dfrac{900}{3}\right]=300$$

Similarly, number of 3-digit numbers, divisible by 4 =$$\left[\dfrac{900}{4}\right]=225$$

Now, number of 3-digit numbers, divisible by both 3 and 4 (means divisible by 12)=$$\left[\dfrac{900}{12}\right]=75$$

Number of 3-digit numbers divisible by either 3 or 4 = $$300+225-75=450$$

So, number of 3-digit numbers divisible by neither 3 nor 4 = $$900-450=450$$

So, probability that the randomly selected number is neither divisible by 3 nor by 4 = $$\dfrac{450}{900}=\dfrac{1}{2}$$