1 of 8 0-day streak

Probability from a uniform area model

Question 1 of 8

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A rectangular object remains inside a rectangular card; its centre is equally likely at any allowable position

The board has width 17 units and height 12 units. The object has width 6 units and height 6 units

The object's sides are parallel to the board's sides

Measure centre positions from the lower-left corner of the allowable centre region. Event \(E\) occurs when the centre lies in a target rectangle with lower-left corner \((7,3)\), width 2 units and height 2 units

w_{c}=17-6=11,\quad h_{c}=12-6=6

(a)1 mark

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

\frac{2\times2}{(17-6)\times(12-6)}

Use the boundary length of the target rectangle divided by the boundary length of the board

\frac{2\times2}{17\times12}

\frac{2\times2}{(17+6)\times(12+6)}

(b)1 mark

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

Area of event region

Format: exact area

Find the area of the complete region of possible locations

Area of complete region

Format: exact area

(d)1 mark

Determine \(Pr(E)\) from the two areas

Exact probability

Format: exact fraction or terminating decimal