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Mathematics · Probability · NCERT Examples

Example 11

A complete, independently verified solution for NCERT Example 11.

Mathematics · Chapter 14 · NCERT Examples

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NCERT Example

Example 11

geometrical probability · area · lake

A missing helicopter is equally likely to have crashed anywhere in the rectangular region shown. Find the probability that it crashed inside the lake.

NCERT marks this example as not from the examination point of view.

Rectangular 9 kilometre by 4.5 kilometre search region containing a rectangular lake; the forest extends 6 kilometres along the top and 2 kilometres up the right side.
Figure 14-2 from the supplied NCERT chapter.

Solution

Board-exam working:

Area of the complete search region:

AR=9×4.5=40.5 km2A_R=9\times4.5=40.5\text{ km}^2

From the labelled dimensions, the lake is 3 km wide and 2.5 km high.

Lake width=9−6=3 km\text{Lake width}=9-6=3\text{ km}
Lake height=4.5−2=2.5 km\text{Lake height}=4.5-2=2.5\text{ km}
AL=3×2.5=7.5 km2A_L=3\times2.5=7.5\text{ km}^2
P(inside lake)=ALAR=7.540.5P(\text{inside lake})=\frac{A_L}{A_R}=\frac{7.5}{40.5}
=75405=527=\frac{75}{405}=\frac5{27}

Final answer

P(inside lake)=527\boxed{P(\text{inside lake})=\frac5{27}}