Question

the figure shows a smaller square within a larger square. a point is chosen at random inside the larger square. what is the probability that this point is in the shaded area? write the answer as a decimal. 10 in. 5 in.

Explanation:

Step1: Calculate area of large square

The side length of the large square is 10 in. The area of a square is given by the formula \( A = s^2 \), where \( s \) is the side length. So, the area of the large square, \( A_{large} = 10^2 = 100 \) square inches.

Step2: Calculate area of small square

The side length of the small square is 5 in. Using the same area formula for a square, the area of the small square, \( A_{small} = 5^2 = 25 \) square inches.

Step3: Calculate the probability

The probability that a randomly chosen point inside the large square is in the shaded area (which is the area of the small square relative to the large square) is given by the ratio of the area of the small square to the area of the large square. So, \( P = \frac{A_{small}}{A_{large}} = \frac{25}{100} = 0.25 \).

Answer:

0.25