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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?

 Apr 14, 2022
 #1
avatar+578 
+2

“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%"

 Apr 14, 2022
 #2
avatar+578 
+2

You can use this as well if needed:

 

https://web2.0calc.com/questions/please-help_56600

 Apr 14, 2022

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