A point is chosen at random inside a rectangle measuring 6 inches

| A point is chosen at random inside a rectangle measuring 6 inches by 5 inches. What is the probability that the randomly selected point is at least one inch from the edge of the rectangle?

A. \(\frac{2}{3}\)

B. \(\frac{1}{3}\)

C. \(\frac{1}{4}\)

D. \(\frac{2}{5}\)

Please scroll down to see the correct answer and solution guide.

Right Answer is: D

SOLUTION

Concept:

Probability = \(\frac{{{\rm{required\;outcome\;}}}}{{{\rm{total\;outcome\;}}}}\)
Area of rectangle of length l and breadth b, A = l × b

Calculation:

Here, total area = 6 × 5 = 30 sq. inch

Now, the randomly selected point is at least one inch from the edge of the rectangle

So, by leaving space of 1 inch inside the original rectangle will give another rectangle of length 4 inch and breadth 3 inch

So, area of required rectangle = 4 × 3 = 12 sq. inch

\(\therefore {\rm{Probability}} = \frac{{{\rm{required\;area\;}}}}{{{\rm{total\;area\;}}}}\)

\(= \frac{{12}}{{30}}\)

\(= \frac{2}{5}\)

Hence, option (4) is correct.