Sector, shaded-region and conditional probabilities on a spinner with unequal sectors

A spinner is a circle split into three sectors, \(A\), \(B\) and \(C\), whose angles at the centre are \(90^\circ\), \(120^\circ\) and \(150^\circ\) respectively, as shown in the diagram. Sectors \(A\) and \(B\) are shaded. The pointer is spun once, and it never comes to rest on a line between two sectors. Let \(A\), \(B\) and \(C\) be the events that the pointer stops in sector \(A\), \(B\) and \(C\) respectively, and let \(S\) be the event that it stops in a shaded sector.

Find

1. \(P(B)\)
2. \(P(S)\)
3. \(P(A\mid S)\)

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