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Question

Suppose that a dart lands at random on the dartboard shown. Find each the theoretical probability.

A.)the dart lands in the bull's eye (20).

B. The dart lands in the green region (10 and 2)

C.) the dart scores at least 10 points (10)

D.) the dart scores less than 10 points (2 and 5)

 

Keys

* bull eyes: 20

*the next circle: 10

*the next one: 5

*the next one (top layer): 2

Answer 1

It is not possible to answer this question without knowing the size of the dartboard and each area.

But assuming that all darts hit the dartboard and that the spot that the hit is random then the probability is given by the ration of the area of each consecutive target divided by the total area.

For example if the bulls eye measures 2 inches in diameter and the total dartboard is 2 foot in diameter the the probability of hitting the bulls eye is given by:  

A (bulls eye)/ A (dartboard)

pi r² (bulls eye)/ pi r² (dartboard)            radius = 1/2 diameter

1² (bulls eye)/ 12² (dartboard)                pi cancels out   

1/144