The probability that a point is chosen at random will lie in the shaded area is 0.32.
Concept:
- Here favorable outcomes will be the shaded portion and the total outcome will be the total circular portion.
How to solve the given question?
- Favorable Outcome = Area of shaded portion = [tex]\frac{1}{2} (18)(\frac{18}{2}) = 81 \ inch^2[/tex]
- Total Outcome = Total area = [tex]\pi \ ( \frac{18}{2} )^{2} = 81 \ \pi \ inch^{2}[/tex]
- ∴ Probability, P(E) = [tex]\frac{81}{81\pi } =\frac{1}{\pi } = 0.32[/tex]
Thus, the probability that a point chosen at random will lie in the shaded area is 0.32.
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