This was an example given in class that wasn\'t in the textbook. I got an answer

Question

This was an example given in class that wasn't in the textbook. I got an answer (45/60) that was different than the one the teacher gave (55/70) but I have no idea why, could anyone help? Problem: Choose 2 uniform numbers without replacement in {0, 1, ..., 10}. What is the probability that the sum is less than or equal to 10 given that the smaller number is less than or equal to 5? She did it by graphing the restrictions and counting the number of points on the inside. I did it by just looking at the individual cases (i.e. if the smaller number is 5 what is the probability that the sum is less than or equal to 10, for 4, 3, etc.). Doing that I got 10/10 + 9/10 + 8/10 + 7/10 + 6/10 + 5/10 for 45/60. Does anyone know a better way to approach this problem and does it yield the answer of 45/60 or 55/70? Thank you.

Explanation / Answer

x.P5 U1 be the value of the first draw, and let U2 be the value of the second draw.

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