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Arturiano [62]
3 years ago
15

A computer consulting firm presently has bids out on three projects. Let Ai = {awarded project i}, for i = 1, 2, 3, and suppose

that P(A1) = 0.22, P(A2) = 0.25, P(A3) = 0.28, P(A1 ∩ A2) = 0.12, P(A1 ∩ A3) = 0.03, P(A2 ∩ A3) = 0.06, P(A1 ∩ A2 ∩ A3) = 0.01. Express in words each of the following events, and compute the probability of each event. (a) A1 ∪ A2
Mathematics
1 answer:
VLD [36.1K]3 years ago
7 0

Answer:

(a) P(A1 ∪ A2) = 0.35

Step-by-step explanation:

(a) A1 ∪ A2 :

We start by defining the events.

A1 : '' awarded project 1''

A2 : ''awarded project 2''

A3: ''awarded project 3''

In set theory we write the union of events A and B as A∪B.

A∪B means that the event A occurs,event B occurs or either both events occurs at the same time.

The probability is given by the equation :

P(A∪B) = P(A) + P(B) - P(A∩B) (1)

Where the event (A∩B) is the event where A and B occur at the same time

and P(A∩B) is the probability of (A∩B)

Using the equation (1) :

P(A1 ∪ A2) = P(A1) + P(A2) - P(A1∩A2)

P(A1 ∪ A2) = 0.22 + 0.25 - 0.12

P(A1 ∪ A2) = 0.35

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The volume of sphere is \frac{1372}{3}\pi feet cubed.

Step-by-step explanation:

Given,

Surface area of sphere = 196π square feet

Surface area of sphere = 4πr²

We will find radius of sphere.

4\pi r^2=196\pi

Dividing both sides by 4π

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Taking square root on both sides

\sqrt{r^2}=\sqrt{49}\\r=7

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Volume of sphere = \frac{4}{3}\pi r^3

Volume=\frac{4}{3}\pi (7)^3\\\\Volume= \frac{4}{3}\pi *343\\\\Volume = \frac{1372}{3}\pi

The volume of sphere is \frac{1372}{3}\pi feet cubed.

Keywords: volume, surface area

Learn more about surface area at:

  • brainly.com/question/101683
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#LearnwithBrainly

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see below

Step-by-step explanation:

A = {8, 9, 10, 11, 12, 13, 14} and   B = {2, 4, 6, 8, 10, 12, 14, 16, 18}

----------------

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{8, 9, 10, 11, 12, 13, 14, 2, 4, 6, 8, 10, 12, 14, 16, 18} - this is the elements of both sets

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