The probability that a randomly selected point within the circle falls in the red-shaded area is 75.61%.
What is the probability?
Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
We need to find the probability that a randomly selected point within the circle falls in the white area.
We have been given the following parameters;
Radius r = 4 cm
a = 3.2 cm
S = 4.7 cm
The area of the circle A = πr²
A = π(4)²
A = 16π square cm
Here, The total number of outcomes = 16π square cm = 50.26 square cm
The side length of the pentagon a = 4.7 cm
The area of the pentagon can be calculated using:
Area = (1/4)√[5(5+2√5)]a²
Plug a = 4.7
Area = (1/4)√[5(5+2√5)](4.7)²
After calculating, we get;
Area = 38.01 square cm
The Total favorable outcomes = 38.01 square cm
The probability = 38.01/50.26
The probability = 0.7561
In percent,
The probability = 75.61%
Therefore, the probability that a randomly selected point within the circle falls in the red-shaded area is 75.61%.
Learn more about probability here;
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