Question

Two numbers are selected at random from $1,2,3,.....100$ and multiplied. Then find the probability that the product thus obtained is divisible by $3$.

Answer 1

Numbers from $1,2,,..100$ not divisible by $3$ are $100-33=67$

Probability that no number is divisible by $3$ is $\frac{{}^{67}{C}_2}{{}^{100}{C}_2}=0.44666$
Then required probability is $1-0.44666=055$