# Pick a box, any box

A room contains 150 boxes. The boxes are identical except for colour. Each box contains a card which has one of three messages printed on it.

In 78 of the boxes the card says “No Prize”. In 66 of the boxes the card says “Winner $20”. And in 6 of the boxes the card says “Winner$100”. Contestants have been assigned a number corresponding to when they will make their selection.

On a turn, each contestant gets to randomly choose 2 boxes. Once a box is chosen it is removed from the room.

You are the second contestant.

If the probability that you will select at least one of the boxes containing a \$100 prize can be expressed as $$\dfrac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

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