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PolarNik [594]
3 years ago
8

A card is drawn at random from a standard deck of 52 cards. Find the following conditional probabilities. ​a) The card is a diam

ond​, given that it is red. ​b) The card is red​, given that it is a diamond. ​c) The card is a nine​, given that it is red. ​d) The card is a king​, given that it is a face card.
Mathematics
1 answer:
Inga [223]3 years ago
7 0

Answer:

a.\frac{1}{13}\\b.\frac{1}{2}\\c.\frac{1}{13}\\d.\frac{1}{13}

Step-by-step explanation:

P(A|B) = P(A and B) / P(B)

Total number of cards = 52

a)

Let A denotes the event that the card is a diamond​ and B denotes the card is red.

P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}\\=\frac{\frac{2}{52}}{\frac{26}{52}}\\=\frac{1}{13}

b)

Let A denotes the event that the card is red​ and B denotes the card is diamond.

P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}=\frac{\frac{2}{52}}{\frac{4}{52}}\\=\frac{1}{2}

c)

Let A denotes the event that the card is nine and B denotes the card is red.

P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}=\frac{\frac{2}{52}}{\frac{26}{52}}\\=\frac{1}{13}

d)

Let A denotes the event that the card is a king and B denotes the card is a face card.

P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}=\frac{\frac{4}{52}}{\frac{12}{52}}\\=\frac{1}{13}

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Answer: 0.02 per year

Step-by-step explanation:

When given the per capita birth rate and the per capita death rate, the per capita growth rate can be calculated as:

= per capita birth rate - per capita death rate

= 0.11 - 0.09

= 0.02/year

= 2% per year

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3 years ago
Please help ill mark brainliest​
anyanavicka [17]

The value of the missing length is 20

Let the missing length be x

From Parallel lines and transversal theorem, we have that

If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally.

Then, we can write that

\frac{x}{15} =\frac{16}{12}

∴ x = \frac{15\times 16}{12}

x = 20

Hence, the value of the missing length is 20

Learn more here: brainly.com/question/24258397

6 0
3 years ago
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Lera25 [3.4K]

Answer:

To construct the Square using a compass and straight edge, you have written the steps not in proper order. I am rearranging the steps for you

1. Construct horizontal ​ H J¯¯¯¯¯

2. ​Construct a circle with point H as the center and a circle with point J as a center with each circle having radius HJ .

3.Label the point of intersection of the two circles above​ ​ HJ¯¯¯¯¯ ​​, point K, and the point of intersection of the two circles below ​ HJ¯¯¯¯¯ ​, point L.

4.Construct KL¯¯¯¯¯ , the perpendicular bisector of ​ HJ¯¯¯¯¯ ​, intersecting​ ​ HJ¯¯¯¯¯ ​ ​​at point M.

5.Construct a circle with point M as the center with radius MJ .

6.Label the point of intersection of circle M and ​ KL¯¯¯¯¯ ​ closest to point K, point N, and the point of intersection of circle M and ​ KL¯¯¯¯¯ ​  closest to point L, point O.

7.Construct HN¯¯¯¯¯¯ , NJ¯¯¯¯¯ , JO¯¯¯¯¯ , and OH¯¯¯¯¯¯ to complete square HNJO .





3 0
3 years ago
The greater of two numbers is six more
pickupchik [31]

Answer:

 

Let's begin by writing the mathematical equations given by the sentences.

 

Let X = smaller number

Let Y = larger number

 

The first sentence tells us

X + Y = 38

 

The second sentence tells us

X = Y/3 + 6

 

Since you weren't given a specific method to use, you can use either the substitution method or the elimination(addition) method, whichever works best for you.

 

Since the 2nd equation has the X isolated, I'm going to isolate the X in the first equation,

X = 38 - Y

 

Since both equations are equal to X, I can set them equal to one another and solve for Y.

Y/3 + 6 = 38 - Y

 

Y + 18 = 114 - 3Y

4Y = 96

Y = 24

 

Then use either of the two original equations to solve for X

X + Y = 38

X + 24 = 38

X = 14

Step-by-step explanation:

PLS MAKE ME AS BRAINLIST

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3 years ago
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