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PSYCHO15rus [73]
3 years ago
5

The Venn diagram shows the results of two events resulting from rolling a number cube.

Mathematics
1 answer:
tankabanditka [31]3 years ago
6 0

Answer:

P(A|B)=\frac{2}{3}

P(A)*P(B)=\frac{1}{3}

P(A) =\frac{2}{3}

P(B) =\frac{1}{2}.

Step-by-step explanation:

We use the Venn diagram to calculate the desired probabilities.

Note that there are 6 possible results in the sample space

S = {1, 2, 3, 4, 5, 6}

Then note that in the region representing the intercept of A and B there are two possible values.

So

P (A\ and\ B) = \frac{2}{6} = \frac{1}{3}

In the region that represents event A there are 4 possible outcomes {4, 5, 1, 2}

So

P(A) = \frac{4}{6} = \frac{2}{3}

In the region that represents event B there are 3 possible outcomes {1, 2, 6}

So

P(B) = \frac{3}{6} = \frac{1}{2}.

Now

P(A | B)=\frac{P(A \ and\ B)}{P(B)}\\\\P(A | B)=\frac{\frac{1}{3}}{\frac{1}{2}}\\\\P(A|B)=\frac{2}{3}

P(A)*P(B)=\frac{2}{3}*\frac{1}{2}=\frac{1}{3}

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Answer:

504 cm squared

Step-by-step explanation:

To find the surface area, find the area of the square base and add it to the area of each triangle face.

Find the area of the base by multiplying base length by base length.

Here the base is 12 x 12 = 144.

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Here the area is 1/2 * 12 * 15 = 90. Since there are 4 faces, the total area is 4 * 90 = 360.

Together the surface area is 360 + 144 = 504.

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3 years ago
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Step-by-step explanation:

1 / 3

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2/3

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Step-by-step explanation:

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