Sometimes, probability questions can be interpreted geometrically, from simple examples like throwing darts to surprising applications like catching the bus!

A point \((a,b)\) is randomly selected within the triangular region enclosed by the graphs of \( 3y + 2x = 6 \), \( x = 0 \) and \( y = 0 \). What is the probability that \( b > a \) ?

Give your answer as a decimal!

Two people stand around a circular duck pond which has radius \(R\) meters. They are placed randomly (uniformly along the circumference of the duck pond) and independently.

What is the probability that they are more than \(R\) meters apart from each other?

If the probability is \( \frac ab\) for coprime positive integers, give the answer as \(a+b\).

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