Two different positive integers less than 100 are randomly chosen and multiplied together. What is the probability that the resulting product is a multiple of 3?
“positive integers less than 100” are 1–99.
For the result to be a multiple of 3, only one of the numbers chosen has to be a multiple of 3.
There is a 66/99 (2/3) chance that the first number isn't a multiple of 3.
There is a 65/98 chance that the second number isn't a multiple of 3 as it cannot be the same one already chosen.
The chance of neither being a multiple of 3 is 2/3 x 65/98 = 1/3 x 65/49 = 65/147
The chance of one of them being a multiple of three (and therefore the two multiplied together being a multiple of 3) is 1–65/147 = 82/147 or approximately 55.8%"