Question

janet is playing a game on a grid that is made up of 25 equally sized squares. some of the squares are shaded. if the probability of picking a point at random in one of the shaded squares is exactly 0.16, how many of the squares are shaded? options: 2, 4, 16, 21

Explanation:

Step1: Recall probability formula

The probability \( P \) of an event is given by \( P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \). Here, the total number of squares (outcomes) is 25, and the probability of picking a shaded square is 0.16. Let \( x \) be the number of shaded squares. So we have the equation \( 0.16 = \frac{x}{25} \).

Step2: Solve for \( x \)

To find \( x \), multiply both sides of the equation by 25: \( x = 0.16\times25 \). Calculating \( 0.16\times25 \), we know that \( 0.16=\frac{16}{100}=\frac{4}{25} \), so \( \frac{4}{25}\times25 = 4 \). Thus, the number of shaded squares is 4.

Answer:

4