Question

geometric probabilities on a grid juan wants to make a new game board that is a grid containing 25 equally sized squares. how many squares should be shaded to create a region with a geometric probability of 0.2? explain.

Explanation:

Step1: Recall geometric probability formula

Geometric probability for a grid (with equally - sized squares) is given by the number of shaded squares ($n$) divided by the total number of squares ($N$). The formula is $P=\frac{n}{N}$.
We know that $P = 0.2$ and $N=25$.

Step2: Solve for the number of shaded squares ($n$)

From the formula $P=\frac{n}{N}$, we can rearrange it to solve for $n$: $n=P\times N$.
Substitute $P = 0.2$ and $N = 25$ into the formula: $n=0.2\times25$.
Calculating $0.2\times25$, we know that $0.2=\frac{1}{5}$, and $\frac{1}{5}\times25 = 5$.

Answer:

The number of squares that should be shaded is 5.