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3 years ago

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Three fair coins are tossed. what is the probability that they are all heads if at least one coin is head,

2 answers:

Olegator [25]3 years ago

4 0

There is your answer hope it helps
$\frac{1}{3}$

EleoNora [17]3 years ago

3 0

Answer:

1/7

Step-by-step explanation:

There are 8 sample points in the sample space. The sample space is

S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}. The event at least one coin is head is compoused

by seven sample points: {HHH, HHT, HTH, THH, TTH, THT, HTT}, then, to obtain the probability of three heads given that we know that at least one coin is head, we should regard the "new sample space" reduced, i.e., we should consider the set with seven sample points as the new sample space. In the new sample space, just one point corresponds to three heads. Therefore the probability we are seeking is 1 out of 7 or 1/7.

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Aubrey wants to buy a new coat that has a regular price of $185. This weekend the coat is on sale at a 33% discount what is the

sweet-ann [11.9K]

Find 33% of 185:

0.33 * 185 = 61.05

Subtract this from the regular price:

185 - 61.05 = 123.95

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3 years ago

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G with the definition of covariance, prove cov[(ay − b),(cy − d)] = accov(x, y ), where x, y are random variables and a, b, c, d

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By definition of covariance,

$\mathrm{Cov}(X,Y)=\mathbb E[(X-\mathbb E[X])(Y-\mathbb E[Y])]$

$\mathrm{Cov}(X,Y)=\mathbb E[XY-\mathbb E[X]Y-X\mathbb E[Y]+\mathbb E[X]\mathbb E[Y]]=\mathbb E[XY]-\mathbb E[X]\mathbb E[Y]$

We have

$\mathbb E[(aX-b)(cY-d)]=\mathbb E[acXY-adX-bcY+bd]$

$=ac\mathbb E[XY]-ad\mathbb E[X]-bc\mathbb E[Y]+bd$

$\mathbb E[aX-b]=a\mathbb E[X]-b$

$\mathbb E[cY-d]=c\mathbb E[Y]-d$

$\mathbb E[aX-b]\mathbb E[cY-d]=ac\mathbb E[X]\mathbb E[Y]-ad\mathbb E[X]-bc\mathbb E[Y]+bd$

Putting everything together, we find the covariance reduces to

$\mathrm{Cov}(aX-b,cY-d)=ac(\mathbb E[XY]-\mathbb E[X]\mathbb E[Y])=ac\mathrm{Cov}(X,Y)$

as desired.

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3 years ago

Every wee, Andrea travels 1,847 miles for her job. if she does his for 4 weeks, how many miles will she have traveled?

Firdavs [7]

She will have traveled 7,388 miles.

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B) x⁴ + x² + 1 solve it

LekaFEV [45]

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At a campground, a rectangular fire pit is 7 feet by 6 feet. What is the area of the largest circular fire that can be made in t

Fittoniya [83]

The area of the circular fire pit is 4096 square inches.

Explanation:

Given that the rectangular fire pit is 7 feet by 6 feet.

We need to determine the area of the largest circular fire that can be made in this fire pit.

The diameter of the circular fire is 6 feet

The radius is given by

$r=\frac{6}{2} =3$

Radius is 3 feet.

The area of the largest circular fire pit can be determined using the formula,

$Area=\pi r^2$

Substituting the values in the formula, we have,

$Area = (3.14)(3)^2$

$=(3.14)(9)$

$Area= 28.26 \ ft^2$

We need to convert feet to inches by multiplying by 12, we get,

$Area = 28.26\times (12)^2$

$Area = 4096.44 \ in^2$

Rounding off to the nearest square inch, we get,

$Area= 4096 \ in^2$

Thus, the area of the circular fire pit is 4096 square inches.

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3 years ago