Question

calculating geometric probabilities juan’s game board is a square with sides that are 50 cm long. the area of the large circle is about 1,963.5 square cm. what is the geometric probability that juan will not score any points? options: 0, 0.215, 0.785, 1

Explanation:

Step1: Calculate area of square

The side length of the square is 50 cm, so the area of the square $A_{square}=50\times50 = 2500$ square cm.

Step2: Determine area for points

The area where Juan scores points is the area of the large circle, which is 1963.5 square cm. So the area where he does not score is $A_{not\ score}=2500 - 1963.5=536.5$ square cm.

Step3: Calculate probability

The geometric probability of not scoring is the ratio of the area where he does not score to the area of the square. So $P=\frac{536.5}{2500}=0.2146\approx0.215$.

Answer:

0.215