Finding probability that the product of numbers is divisible by $3$? This is the question given in my text-book From the numbers $$(1, 2, 3,....,50)$$ two numbers are selected at random and multiplied. Find the probability that the product thus obtained , is a multiple of 3 ? I have no idea how to do it can anybody help me Thanks

$3$ being prime, at least one of the numbers chosen must be divisible by $3$. There are $16$ such numbers.

The probability of choosing _at least_ one number divisible by $3$ is $1$ minus the probability of choosing no numbers divisible by $3$. Thus we have,

$$1-\frac{34}{50}\cdot\frac{33}{49}=\frac{1328}{2450}$$

**EDIT** : The above assumes that we aren't allowed to pick the same number twice, i.e, $1$ and $1$ isn't a valid choice. In case that is valid, our probability would be,

$$1-\frac{34}{50}\cdot\frac{34}{50}=\frac{1344}{2500}$$