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3 years ago

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If a couple were planning to have three children, the sample space summarizing the gender outcomes would be: bbb, bbg, bgb,

bgg, gbb, gbg, ggb, ggg. a. Construct a similar sample space for the possible health outcomes (using h for healthy and s for sick) of two children. b. Assuming that the outcomes listed in part (a) were equally likely, find the probability of getting two healthy children. c. Find the probability of getting exactly one healthy child and one sick child. a. What is the sample space?

1 answer:

harkovskaia [24]3 years ago

6 0

Answer:

a.S={hh,sh,hs,ss}

b.tex]\frac{1}{4}[/tex]

c. $\frac{1}{2}$

Step-by-step explanation:

We are given that a sample space of three children

S={bbb,bbg,bgb,bgg,gbb,gbg,ggb,ggg}

a.We have to construct similar space for two children where h for healthy and s for sick.

Then the sample space of two children

S={hh,sh,hs,ss}

b.Number of cases favorable to two healthy children=1

Total number of cases=4

Number of cases for two healthy children=1

Probability =Number of favorable cases divided by total number of cases

Probability= $\frac{1}{4}$

Hence, the probability of getting two healthy children= $\frac{1}{4}$

c.We have to find the probability of getting exactly one healthy child and one sick child

Number of cases of one healthy child and one sick child={hs,sh}=2

Probability= $\frac{2}{4}=\frac{1}{2}$

Hence, the probability of getting exactly one healthy child and one sick child= $\frac{1}{2}$

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The number of non-blue marbles you need to combine with the blue marbles to achieve a probability of 0.1 is 28.

<h3>How many non-blue marbles are needed?</h3>

Probability determines the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

Probability of picking a blue marble = number of blue marble / total number of marbles

4 / (4 + 8)

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4 years ago

A quadrilateral has vertices at $(0,1)$, $(3,4)$, $(4,3)$ and $(3,0)$. Its perimeter can be expressed in the form $a\sqrt2+b\sqr

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Answer:

a + b = 12

Step-by-step explanation:

Given

Quadrilateral;

Vertices of (0,1), (3,4) (4,3) and (3,0)

$Perimeter = a\sqrt{2} + b\sqrt{10}$

Required

$a + b$

Let the vertices be represented with A,B,C,D such as

A = (0,1); B = (3,4); C = (4,3) and D = (3,0)

To calculate the actual perimeter, we need to first calculate the distance between the points;

Such that:

AB represents distance between point A and B

BC represents distance between point B and C

CD represents distance between point C and D

DA represents distance between point D and A

Calculating AB

Here, we consider A = (0,1); B = (3,4);

Distance is calculated as;

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$(x_1,y_1) = A(0,1)$

$(x_2,y_2) = B(3,4)$

Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$AB = \sqrt{(0 - 3)^2 + (1 - 4)^2}$

$AB = \sqrt{( - 3)^2 + (-3)^2}$

$AB = \sqrt{9+ 9}$

$AB = \sqrt{18}$

$AB = \sqrt{9*2}$

$AB = \sqrt{9}*\sqrt{2}$

$AB = 3\sqrt{2}$

Calculating BC

Here, we consider B = (3,4); C = (4,3)

Here,

$(x_1,y_1) = B (3,4)$

$(x_2,y_2) = C(4,3)$

Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$BC = \sqrt{(3 - 4)^2 + (4 - 3)^2}$

$BC = \sqrt{(-1)^2 + (1)^2}$

$BC = \sqrt{1 + 1}$

$BC = \sqrt{2}$

Calculating CD

Here, we consider C = (4,3); D = (3,0)

Here,

$(x_1,y_1) = C(4,3)$

$(x_2,y_2) = D (3,0)$

Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$CD = \sqrt{(4 - 3)^2 + (3 - 0)^2}$

$CD = \sqrt{(1)^2 + (3)^2}$

$CD = \sqrt{1 + 9}$

$CD = \sqrt{10}$

Lastly;

Calculating DA

Here, we consider C = (4,3); D = (3,0)

Here,

$(x_1,y_1) = D (3,0)$

$(x_2,y_2) = A (0,1)$

Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$DA = \sqrt{(3 - 0)^2 + (0 - 1)^2}$

$DA = \sqrt{(3)^2 + (- 1)^2}$

$DA = \sqrt{9 + 1}$

$DA = \sqrt{10}$

The addition of the values of distances AB, BC, CD and DA gives the perimeter of the quadrilateral

$Perimeter = 3\sqrt{2} + \sqrt{2} + \sqrt{10} + \sqrt{10}$

$Perimeter = 4\sqrt{2} + 2\sqrt{10}$

Recall that

$Perimeter = a\sqrt{2} + b\sqrt{10}$

This implies that

$a\sqrt{2} + b\sqrt{10} = 4\sqrt{2} + 2\sqrt{10}$

By comparison

$a\sqrt{2} = 4\sqrt{2}$

Divide both sides by $\sqrt{2}$

$a = 4$

By comparison

$b\sqrt{10} = 2\sqrt{10}$

Divide both sides by $\sqrt{10}$

$b = 2$

Hence,

a + b = 2 + 10

a + b = 12

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3 years ago

What property is this: 3 * 1/3 = 1

Rama09 [41]

Answer:

Inverse property of multiplication

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3 years ago

PLEASE HELP IT'S DUE TODAY-

Marina86 [1]

bro.. i don't think someone is gonna answer all this for you, you should like figure this out on ur own..

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3 years ago

Read 2 more answers