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
