Final answer:
The probability that a randomly selected point within the circle falls in the red shaded area is found by dividing the angle of the sector by the full circle. By calculation, it is 165/360, which roughly equals 0.4583. The closest answer choice given is option A, 0.452.
This correct answer is A.
Step-by-step explanation:
The question involves calculating a probability within a geometric context, specifically involving proportions of areas in a circle.
The probability that a randomly selected point within the circle falls in the red shaded area, corresponding to a 165-degree sector, is found by calculating the ratio of the angle of the red-shaded sector to the full 360-degree circle.
Since the angle for the red-shaded area is 165 degrees, the probability that a randomly selected point falls within this area is 165/360.
Using a calculator, you would compute this as:
- Probability = (Angle of red-shaded sector) / (Total degrees in a circle)
- Probability = 165 / 360
- Probability = 0.4583 (rounded to four decimal places)
The closest answer to the calculated probability (0.4583) is option A, which is 0.452.
This correct answer is A.