Wish for Well

Algebra Level 4

A wishing well is located at the point (11, 11) in the xy-plane. Sanket randomly selects an integer y from the set {0, 1, . . . , 10}. Then he randomly selects, with replacement, two integers a, b from the set {1, 2, . . . , 10}. The probability the line through (0, y) and (a, b) passes through the well can be expressed as m/ n , where m and n are relatively prime positive integers. Compute m + n.

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