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3 years ago

Explain pls and thanks

Mathematics

1 answer:

murzikaleks [220]3 years ago

7 0

Starting more simply, if we wanted to know how many students like pink in general, that's 68/100. We could do that for each single category and the fractions would add together to equal 1. Now say we wanted to know something about that 68/100 people. That 68 is our new 100%, or another way of looking at it is if we take however many people like pink and don't like black and those that do like black, they will equal 68/68.

The number of people that like pink but don't like black is 41/68 and those that like pink and black are 27/68. 27+41=68 For the question of your problem it is asking about those that do not like pink which you can tell from the table or use from my saying 68/100 like pink is 32. Now you can split that into those that do or don't like black, and the two results will equal 32/32.

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The prior probabilities for events A1 and A2 are P(A1) = 0.20 and P(A2) = 0.80. It is also known that P(A1 ∩ A2) = 0. Suppose P(

Umnica [9.8K]

Answer:

(a) $A_1$ and $A_2$ are indeed mutually-exclusive.

(b) $\displaystyle P(A_1\; \cap \; B) = \frac{1}{20}$ , whereas $\displaystyle P(A_2\; \cap \; B) = \frac{1}{25}$ .

(d) $\displaystyle P(A_1 \; |\; B) \approx \frac{5}{9}$ , whereas $P(A_1 \; |\; B) = \displaystyle \frac{4}{9}$

Step-by-step explanation:

$P(A_1 \; \cap \; A_2) = 0$ means that it is impossible for events $A_1$ and $A_2$ to happen at the same time. Therefore, event $A_1$ and $A_2$ are mutually-exclusive.

By the definition of conditional probability:

$\displaystyle P(B \; | \; A_1) = \frac{P(B \; \cap \; A_1)}{P(B)} = \frac{P(A_1 \; \cap \; B)}{P(B)}$ .

Rearrange to obtain:

$\displaystyle P(A_1 \; \cap \; B) = P(B \; |\; A_1) \cdot P(A_1) = 0.25 \times 0.20 = \frac{1}{20}$ .

Similarly:

$\displaystyle P(A_2 \; \cap \; B) = P(B \; |\; A_2) \cdot P(A_2) = 0.80 \times 0.05 = \frac{1}{25}$ .

Note that:

$\begin{aligned}P(A_1 \; \cup \; A_2) &= P(A_1) + P(A_2) - P(A_1 \; \cap \; A_2) = 0.20 + 0.80 = 1\end{aligned}$ .

In other words, $A_1$ and $A_2$ are collectively-exhaustive. Since $A_1$ and $A_2$ are collectively-exhaustive and mutually-exclusive at the same time:

$\displaystyle P(B) = P(B \; \cap \; A_1) + P(B \; \cap \; A_2) = \frac{1}{20} + \frac{1}{25} = \frac{9}{100}$ .

By Bayes' Theorem:

$\begin{aligned} P(A_1 \; |\; B) &= \frac{P(B \; | \; A_1) \cdot P(A_1)}{P(B)} \\ &= \frac{0.25 \times 0.20}{9/100} = \frac{0.05 \times 100}{9} = \frac{5}{9}\end{aligned}$ .

Similarly:

$\begin{aligned} P(A_2 \; |\; B) &= \frac{P(B \; | \; A_2) \cdot P(A_2)}{P(B)} \\ &= \frac{0.05 \times 0.80}{9/100} = \frac{0.04 \times 100}{9} = \frac{4}{9}\end{aligned}$ .

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3 years ago

The width of a rectangular flower shop is 20 feet less than twice the length. The perimeter is more than 70 feet. Which inequali

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Answer:

what is it

Step-by-step explanation:

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3 years ago

The length of a rectangular garden is 3 inches greater than twice it’s width find the dimensions if the perimeter is 24 inches

mel-nik [20]

Answer:

width=3

length=9

Step-by-step explanation:

1/2 perimeter: 24/2=12

let x: width; y: lenght

y=2x+3

x=12-y

y=2(12-y)+3

y=24-2y+3

y+2y=27

y=9

x=12-9=3

4 0

3 years ago

The areas of two similar triangles are 72dm2 and 50dm2. The sum of their perimeters is 226dm. What is the perimeter of each of t

zloy xaker [14]

Answer:

103= p small

plarge = 123

Step-by-step explanation:

We know that the the ratio of the areas is the scale factor squared/

Larger triangle over smaller triangle

----- = scale factor ^2

simplify by dividing by 2 on top and bottom

----- = scale factor ^2

Take the square root of each side

sqrt(36)

-------------- = sqrt(scale factor ^2)

sqrt(25)

-------------- = scale factor

The ratio of the perimeters is the scale factor

p large 6

-------------- = ----------------

p small 5

Using cross products

6 p large = 5 p small

We know the sum is 226

p large + p small = 226

p large = 226 - p small

We have 2 equation and 2 unknowns

6 p large = 5 p small

Substitute for p large

6 (226 - p small) = 5 p small

1356 - 6 p small = 5 p small

Add 6 p small to each side

1356 = 11 p small

divide by 11

1356/11 = p small

P large = 226-1356/11

p large = 2486/11-1356/11

plarge = 1130/11

The solution requires whole number answers so

1356/11 = p small

123.27 which rounds to 123

plarge = 1130/11

plarge = 102.7272 = 103

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For the equation y=7x-2, what is the rate of change? What does it mean? It is a linear function where the rate of change is the

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The rate of change would be 7. you would plot your first point on the graph at (-2,0) and the next one would be up 7 and over 1 for your next plot point.

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4 years ago