Number System

Divisibility Rules

Easy

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

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{2}{3}$

$\frac{1}{3}$

✅ Correct Option: 2

Every 3rd number is divisible by 3.

Think about it: 100, 101, 102, 103, 104, 105, 106, 107, 108,...

Probability(number not divisible by 3) $= {\dfrac23}$

Similarly, every 4th number is divisible by 4.

Probability(number not divisible by 4) $= {\dfrac34}$

$\therefore \$ Probability(number not divisible by 3 nor 4) $=\dfrac23 \times \dfrac34 = \boxed{\frac12}$

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