Question 698120: We have to select 2 numbers from 1 to 9. Probability that the product of these 2 numbers is 12, will be
Answer by Positive_EV(69)   (Show Source):
You can put this solution on YOUR website! For the purposes of this equation, I am assuming the numbers selected are integers, and that two different numbers are being chosen.
The probability that the product of two numbers from 1-9 have a product of 12 is equal to the probability that the first number divides evenly into 12 (if you draw a number that does not, there is no second number that can make the product 12) times the probability that the second number makes the product equal to 12.
Between 1-9, the numbers 1, 2, 3, 4, and 6 divide into 12. However, if you draw a 1, you'd need a 12 for the second number which is impossible, so 1 can't be drawn either. Thus, the first draw must be a 2, 3, 4, or 6. The probability you draw one of these numbers is 4/9.
Each of those numbers has one specific number that pairs with it to make a product of 12: 2 requires a 6, 3 requires a 4, 4 requires a 3, and 6 requires a 2. So, no matter what you drew first pick, there's only one number you can draw with your second pick to make the product equal to 12. The probability of getting this number is 1/8, since there are 8 numbers you haven't drawn yet.
The probability the product is 12 is the product of the probability you get a 2, 3, 4, or 6 on draw 1 times the probability you get its match on draw 2, which is (4/9)*(1/8) = (4/72) = (1/18).
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