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In Bullseye question from Probability

In Bullseye question from Probability

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Hi there i am bit poor at probability so i have doubt on bullseye numerical outcomes question.
how does probability of A is 0.5, similarly B is 0.4 and C is 0.1.
pls clarify this doubt of mine.
 
Thanks 

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365 Team
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Hey Aravind, 
 
Thanks for reaching out!
 
So, the focus of that particular lecture is about expected values, so we’re just being “given” the probabilities of each outcome. The idea was to assume that the probabilities of events A, B and C are so and so, and focus on the expected value formula. 
 
However, the rationale we used for the ballpark figure probabilities came from what part of the area of the dart board they cover (assuming each region is equally wide). Hence, if the inner radius is 1, the intermediate one is 2 and the outer most is 3, then the areas of the 3 zones would be:
1.) 1^2*pi = pi
2.) 2^2*pi – (area of the inner circle) = 4*pi – pi = 3*pi
3.) 3^2*pi – (area of the first two layers) = 9*pi – 4*pi = 5*pi
 
Thus, the ratio of the 3 zones, would be 1:3:5. To make the numbers “nicer”, we tweaked it to 1:4:5 and got 0.1, 0.4 and 0.5 respectively.
 
Hope this helps understand our rationale. 
 
Best, 
365 Vik