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Probability from a uniform area model

DIFFICULTYchallenge
Question 1 of 8

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A point is selected uniformly from a rectangular floor

The complete rectangle has width 12 units and height 19 units

Event \(E\) occurs when the point lies in a smaller rectangle with lower-left corner \((3,1)\), width 7 units and height 13 units

A Cartesian diagram of a complete rectangle with vertices (0, 0), (12, 0), (12, 19), (0, 19) and a smaller rectangle with vertices (3, 1), (10, 1), (10, 14), (3, 14).246810120369121518horizontal positionvertical position
(a)1 mark

Which expression or statement correctly represents the probability of event \(E\) under the stated uniform-location model?

(b)1 mark

Find the area of the region that represents event \(E\)

Format: exact area
(c)1 mark

Find the area of the complete region of possible locations

Format: exact area
(d)1 mark

Calculate \(Pr(E)\) as an exact probability

Format: exact fraction or terminating decimal