SEAMO 2027 - Paper E - SET 02 - Self-study Question 14

Question 14

Two numbers are selected at random from $1,2,3,\ldots,100$ and multiplied together. Find the probability that the product is divisible by $3$.

Practice convention: select two distinct numbers uniformly, without replacement. The source does not explicitly say whether replacement is allowed.

$7/15$
$3/4$
$27/50$
$83/150$
$17/30$