darts are thrown at a circular dartboard. of a dart hits the board, what is the probability that the darts land in the bulls-eye

Answers

Answer 1

The probability that out of four darts thrown at the dart board, exactly two hit the bull’s eye: 6

Suppose a circular dart board is 18 inches in diameter, and the bull’s eye in the center is 2 inches in diameter.

The area of the board is:

[tex]A_b = \pi r^2=81\pi[/tex]

but the area of the bulls-eye is:

[tex]A_e=\pi r^2=\pi[/tex]

So the probability that any dart hits the bulls-eye is:

[tex]P=\frac{A_e}{A_b} =\frac{\pi }{81\pi } =\frac{1}{81}[/tex]

Now, to find the probability that exactly two darts hits the bulls-eye, first note there are exactly [tex]\left[\begin{array}{ccc}4\\2\\\end{array}\right][/tex] (read 4 choose 2) ways to choose exactly two darts from the four. This is defined as:

[tex]\left[\begin{array}{ccc}4\\2\\\end{array}\right]=\frac{4!}{2!(4-2)!} =6[/tex]

Second, the probability that exactly two darts (in any order) hit the center is given by:

P . P . (1 - P) . (1- P) = 6400/43046721

Since there six ways to find arrange the darts and have this happen, the final probability of exactly two darts hitting the bulls-eye is given by:

[tex]6\frac{6400}{43046721}[/tex] = 0.0892054%

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The given question is incomplete, complete question is:

Suppose a circular dart board is 18 inches in diameter, and the bull’s eye in the center is 2 inches in diameter. What is the probability that out of four darts thrown at the dart board, exactly two hit the bull’s eye? Assume that each dart lands at a uniformly random point on the board, independently of the other darts.

Answer 2

Answer: d

Explanation: your welcome

Related Questions

Repeated episodes of supercontinent formation and breakup are an example of _________ change.
A) catastrophic,unidirectional
B) gradual,unidirectional
C) catastrophic,cyclic
D) gradual,cyclic

Answers

Repeated episodes of supercontinent formation and breakup are an example of gradual and cyclic change. Option D is the correct answer.

Plate tectonics, volcanism, and the formation of mountains are a few of the geological processes that shape the Earth's crust. The gradual and cyclic motion of tectonic plates, which are large rock slabs that make up the Earth's crust, is what gives rise to and breaks apart supercontinents. Option D is the correct answer.

While these plates are being forced together, other factors have the ability to separate them in the future, leading to the breakup of the supercontinent and the formation of new ones. The process of supercontinent formation and breakup is how supercontinents originate and dissolve, and it is a part of a larger process known as the Wilson Cycle, which illustrates the continuous opening and closing of ocean basins as well as the growth and dissolution of supercontinents throughout time.

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the fact that the amount of ultraviolet radiation (uvr) that reaches different parts of the world has led to the evolution of differences in skin color is an example of which of the following?

Answers

The fact that the amount of ultraviolet radiation (uvr) that reaches different parts of the world has led to the evolution of differences in skin color is an example of distal cause.

A factor or event that is further away in time or space from the initial cause of a specific outcome or behavior is referred to as a distal cause. It is an underlying or secondary factor that affects the development of an event or condition. Distal causes are frequently linked to broader, longer-term factors that influence the environment and circumstances in which particular actions or behaviors take place.

Distal causes offer a more thorough understanding of the factors that contribute to a particular phenomenon than proximal causes, which are immediate and directly connected to a particular outcome. They might include socioeconomic, cultural, historical, or environmental variables that operate over a long time and have a more tangential impact on the observed result.

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The question is incomplete, complete question is "the fact that the amount of ultraviolet radiation (uvr) that reaches different parts of the world has led to the evolution of differences in skin color is an example of which of the following?

distal cause

proximal cause

vitamins and rest

biological variation"

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