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Suppose you have a dart board hanging on a wall If you throw a dart randomly at the wall, and assuming your dart lands somewhere on the wall , what is the probability that your dart will land a) in region X b) in region c) in region Z

Suppose You Have A Dart Board Hanging On A Wall If You Throw A Dart Randomly At The Wall And Assuming Your Dart Lands Somewhere On The Wall What Is The Probabil class=

Sagot :

MrRoyal

Probabilities are used to determine the chances of events

  • The probability of landing in region X is 0.087
  • The probability of landing in region Y is 0.109
  • The probability of landing in region Z is 0.153

The probability of landing in region X

The area of region X is:

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

So, we have:

[tex]X = 3.14 * 4^2[/tex]

[tex]X = 50.24[/tex]

The area of the dart is:

[tex]A = Length * Width[/tex]

[tex]A = 24 * 24[/tex]

[tex]A = 576[/tex]

The probability of landing in region X is then calculated as:

[tex]P(X) = 50.24/576[/tex]

[tex]P(X) = 0.087[/tex]

The probability of landing in region Y

The area of region Y is:

[tex]A = \pi R^2 - \pi r^2[/tex]

So, we have:

[tex]Y = 3.14 * 6^2 -3.14 *4^2[/tex]

[tex]Y = 62.8[/tex]

The probability of landing in region Y is then calculated as:

[tex]P(Y) =62.8/576[/tex]

[tex]P(Y) =0.109[/tex]

The probability of landing in region Z

The area of region Z is:

[tex]A = \pi R^2 - \pi r^2[/tex]

So, we have:

[tex]Z = 3.14 * 8^2 -3.14 *6^2[/tex]

[tex]Z = 87.92[/tex]

The probability of landing in region Z is then calculated as:

[tex]P(Z) = 87.92/576[/tex]

[tex]P(Z) = 0.153[/tex]

Hence, the probability of landing in region Z is 0.153

Read more about probabilities at:

https://brainly.com/question/25870256

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