A certain dartboard is a disk of radius 3 with circles of radius 1 and 2 drawn inside it. The area inside the circle of radius 1 is shaded blue; the area between the two circles is shaded white; the area outside the circle of radius 2 is shaded red, as shown below. You throw a dart at the dartboard. Your aim is not very good, so the dart is equally likely to land anywhere on the dartboard (but at least you are guaranteed not to miss the dartboard entirely). The formula for the area of a circle is A = r², where r is the radius. a.) Find the probabilities of the dart landing in each of the three regions: red, white, and blue. b.) What is the conditional probability of the dart landing inside the blue region, given that the dart doesn't land in the red region?
A certain dartboard is a disk of radius 3 with circles of radius 1 and 2 drawn inside it. The area inside the circle of radius 1 is shaded blue; the area between the two circles is shaded white; the area outside the circle of radius 2 is shaded red, as shown below. You throw a dart at the dartboard. Your aim is not very good, so the dart is equally likely to land anywhere on the dartboard (but at least you are guaranteed not to miss the dartboard entirely). The formula for the area of a circle is A = r², where r is the radius. a.) Find the probabilities of the dart landing in each of the three regions: red, white, and blue. b.) What is the conditional probability of the dart landing inside the blue region, given that the dart doesn't land in the red region?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:A certain dartboard is a disk of radius 3 with circles of radius 1 and 2 drawn inside it. The area
inside the circle of radius 1 is shaded blue; the area between the two circles is shaded white; the
area outside the circle of radius 2 is shaded red, as shown below.
You throw a dart at the dartboard. Your aim is not very good, so the dart is equally likely
to land anywhere on the dartboard (but at least you are guaranteed not to miss the dartboard
entirely).
The formula for the area of a circle is A = 7², where r is the radius.
a.) Find the probabilities of the dart landing in each of the three regions: red, white, and
blue.
b.) What is the conditional probability of the dart landing inside the blue region, given
that the dart doesn't land in the red region?
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