Question

The figure below shows a shaded rectangle inside a large rectangle: A rectangle of length 10 units and width 5 units is shown. Inside this rectangle is another rectangle of length 9 units and width 3 units placed symmetrically inside the larger rectangle. The smaller rectangle is shaded gray. If you choose a point inside the large rectangle, what is the probability that it is not inside the shaded rectangle?

Answer 1

Answer: $\dfrac{7}{10}$

Step-by-step explanation:

Given : The length of larger rectangle = 10 units

The width of larger rectangle = 5 units

The area of the larger rectangle will be :-

$A=5\times10=50\text{ units}^2$

The length of smaller rectangle = 9 units

The width of the smaller rectangle = 3 units

The area of the smaller rectangle will be :-

$A=3\times9=27\text{ units}^2$

Now, the probability that it is inside the shaded rectangle :-

$\dfrac{27}{90}=\dfrac{3}{10}$

Then , the probability that it is not inside the shaded rectangle will be:-

$1-\dfrac{3}{10}=\dfrac{7}{10}$

Answer 2

100/50 = x/27
50x=2700
x=54   (small rectangle is 54% of the large rectangle
100% - 54% =46%  (46% is not shaded)
Probability     46%   or 23/50