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  4. A three-digit number was chosen at random. What is the the probability that it is divisible by both 2 and 3.

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Q. A three-digit number was chosen at random. What is the the probability that it is divisible by both 2 and 3.

Probability

Solution:

Let the number be $x, 100 \leq x \leq 999$. (There are 900 three digits numbers)
A number divisible by both 2 and 3 must be divisible by the LCM of $(2,3)=6$.
Least value of $x$ divisible by $6=102=6(17)$
Greatest value of $x$ divisible by $6=996=$ $6(166)$
There are 150 values of $x$ divisible by 6 .
Required probability $=\frac{150}{900}=\frac{1}{6}$