The probability that the first slice of the cake will contain the marble is 7/66
How to determine the probability using parts A and B?
The complete question is in the attached image
The part A of the question requires that the volume of the cake be calculated
The volume of the cake is:
[tex]V = \pi (d/2)^2h[/tex]
[tex]V = \pi (9/2)^2 * 4[/tex]
Evaluate
[tex]V = 81\pi[/tex]
The part B of the question requires that the volume of each cut be calculated
The volume of each cut is:
V = 27
Now, to determine the required probability
We simply divide the volume of each cut by the volume of the cake.
i.e.
[tex]P = \frac{27}{81\pi}[/tex]
This gives
[tex]P = \frac{1}{3\pi}[/tex]
Expand π
[tex]P = \frac{7}{3 * 22}[/tex]
[tex]P = \frac{7}{66}[/tex]
Hence, the probability that the first slice of the cake will contain the marble is 7/66
Read more about probability at:
https://brainly.com/question/24756209
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