NCERT Example 11 — Probability

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:

A_R=9\times4.5=40.5\text{ km}^2

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

\text{Lake width}=9-6=3\text{ km}

\text{Lake height}=4.5-2=2.5\text{ km}

A_L=3\times2.5=7.5\text{ km}^2

P(\text{inside lake})=\frac{A_L}{A_R}=\frac{7.5}{40.5}

=\frac{75}{405}=\frac5{27}

Final answer

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

Example 11

Example 11

Solution

Final answer

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