Seeing The Red Pin

Bowling pins are arranged in a triangular array of 10 pins. From the perspective of a bowler at one end of the lane, he cannot see all 10 pins on the other end because some are obscured from sight (as seen in the picture).

A pinsetter is used to replace the bowling pins. There are often more than 10 pins in the machine at any one time to allow for quicker pin setup. Suppose that there are 15 pins in a pinsetter, 14 white pins and 1 red pin. The pinsetter randomly chooses and sets 10 of them on the lane in the typical triangular arrangement. If the probability that the bowler can see the red pin is \(\frac{a}{b}\), where \(a\) and \(b\) are positive coprime integers, then what is the value of \(a+b\)?

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