Question

A missing helicopter is reported to have crashed somewhere in the rectangular region shown in figure. What is the probability that it crashed inside the lake shown in the figure.

Answer 1

Hint: For solving this question you should know about the area of a rectangular and finding the probability for this. So, the area of the rectangle is equal to multiply of length with breadth and then we will find the probability for this. And this will be our final answer for this.

Complete step-by-step solution:
According to the question it is given that a missing helicopter is reported to have crashed somewhere in the rectangular region shown in figure. Then what will be the probability for this that the helicopter crashed inside the lake.
So, if we look at the figure then it is clear that the lake is in a rectangular area and whose range is given to us. And the dimensions of the lake are not given. Then first we will find the dimension of the lake and then we will find the area of this
So, the complete length of the field = 9 km
And the breadth of the rectangular field = 4.5 km
So, if we find the area of the field then: area of field = length * breadth
\[\begin{align}
  & =9\times 4.5 \\
 & =40.5k{{m}^{2}} \\
\end{align}\]
Now, dimension of the lake are:
Since, the lake is in corner of field , so according to the diagram the length of field is 9 km = (6 + x) km
\[\Rightarrow x=3\] km
So, the length of lake is 3km
 And breadth of lake \[y=4.5-2=2.5\]km
So, the area of the lake \[=3\times 2.5=7.5k{{m}^{2}}\]
So, the probability of becoming crash of helicopter in lake is: \[P\left(\dfrac{a}{A} \right)=\dfrac{7.5}{40.5}=0.18\]
Thus, the probability that it crashed inside the lake is 0.18.

Note: During solving these types of questions you should be careful for the dimensions of that. If there is any other shape in that first figure then first try to find the dimensions of this and then find the area or volume for that.