Question

given a grid with 15 sections, determine how many sections in the grid need to be shaded so the probability of a point chosen at random in the shaded area is exactly 0.8. explain your reasoning.

Explanation:

Step1: Recall probability formula

The probability \( P \) of a random point being in the shaded area is the number of shaded sections \( n \) divided by the total number of sections \( N \), so \( P=\frac{n}{N} \).

Step2: Substitute known values

We know \( P = 0.8 \) and \( N=15 \). Substitute into the formula: \( 0.8=\frac{n}{15} \).

Step3: Solve for \( n \)

Multiply both sides by 15: \( n = 0.8\times15 \). Calculate \( 0.8\times15 = 12 \). So 12 sections need to be shaded.

Answer:

12