Ignoring leap days, the days of the year can be numbered 1 to 365. Assume that birthdays are equally likely to fall on any day of the year. Consider a group of 10 people, of which you are not a member. The sample space consists of all possible sequences of 10 birthdays (onefor each person).

a. Define the probability function P for S.
b. Consider the following events:
1. "someone in the group shares your birthday";
2. "some two people in the group share a birthday";
3. "some three people in the group share a birthday". Carefully describe the subset of S that corresponds to each event.

c. Find an exact formula for P(A). What is the smallest m such that P(A) > .5?
d. Justify why m is greater than 365 without doing any computation. (We 3 are looking for 2 a short answer giving a heuristic sense of why this is so.)
e. Find an exact formula for P(B).

Answers

Answer 1

Answer:

Follows are the solution to the given question:

Step-by-step explanation:

They can count the days of the year 1 to 365. The random project consists of drawing a sample of n objects from D where elements are n people's birth in a group but instead, D = {1,....365}. And then there's the issue.

[tex]S=365^n[/tex]

This because the list of future birthdays of n people was its test point; therefore m points will be in the sequence so each point contains 365 distinct outcomes. The probability function P for \Omega is that any event is likely to happen in 365 days.

[tex]P(x)=\frac{1}{365^{n}}[/tex]

if x is between 1 and 365 as well as the occurrence is just all similarly possible

In point i:

That somebody mentions their birthday throughout the party

Guess I was born on day b. Therefore the consequence of "x is in A" is "b is now in the series of x," which is to say, b = bk for some amount k approximately 1 and n.

In point ii:

Any 2 persons share the same birthday at this party". A result x is in B" means which "two of entries in x are same." This means that perhaps the outcome x is in B if or only if bj = bk is in B of two numbers j, and k of 1, of two. , no, n.

In point iii:

Many three students share the same birthday with both the party. The consequence is x at the level of C only when bj = bk = bl at three (different) indices, j, k, l, 1. , no, n.


Related Questions

A scientist wants to measure out .62liters of a liquid, but she can only find a beaker that measures volume in milliliters. How many milliliters should she measure to equal .62liters?

Answers

Answer:

620 milliliters

Step-by-step explanation:

1 milliliter= 0.001 liters

0.62L= move the decimal point 3 places to the left

0.62

06.2

062.

0620.

620 milliliters

s - k + x; when s = 7, k = 4, x = 6


what does this mean someone help quick

Answers

Answer:

you just plug in those numbers... 7-4+6 = 9

factor the expression-15x +39​

Answers

Answer:

3(5−13)

Step-by-step explanation:

..............

Answer:

-3(5x-13)

Step-by-step explanation:

The greatest common factor is 3 and you want the # with the variable to be positive, usually, so just factor -3 out and that's what you get.

Which side lengths form a right triangle?
Choose all answers that apply:
A
3.4.5
B
7.8.9
3.9.95

Answers

Answer:

A. 3.4.5

Step-by-step explanation:

I looked it up and it forms a right angle.

Team A scored the following points per game 20,17,25,25,13,25,12,25,25 and 23 team B scored the following points per game 25,25,9,10,25,11,25,15,10 and 25 what is the mean of team A and team B

Answers

Answer:

Mean of team A = 21

Mean of team B = 18

Step-by-step explanation:

Formula:

Mean = Sum of values / Number of values

Calculations:

[tex]A = \frac{20+17+25+25+13+25+12+25+25+23}{10} = \frac{210}{10} = 21[/tex]

[tex]B = \frac{25+25+9+10+25+11+25+15+10+25}{10} =\frac{180}{10} =18[/tex]

Mean of team A = 21

Mean of team B = 18

If the turning point is lower than the nearby point it's called a

Answers

Answer:

Step-by-step explanation:

Local minimum. It would be the minimum value of the function not including the end points. If you are including the end points, its an absolute minimum

What is 2(x -3) in simplest form?

Answers

Answer:

2x-6 is the right answer

Step-by-step explanation:

I'm very good at math

If 210 people said football was their favorite sport to watch, how many people were surveyed? 42% said football.

Answers

Answer:

500 people surveyed

Step-by-step explanation:

210 / 42 = 5

5 x 100 = 500

Answer:

500 people were surveyed

Step-by-step explanation:

Let the total number of people surveyed be x

42% said football was their favorite sport to watch

=> 42/100 x = 210

=> x = (210 × 100) / 42

=> x = 21000 / 42

=> x = 500

Therefore, 500 people were surveyed.

Hope it helps :)

Please mark my answer as the brainliest

3.) The ratio of dogs to cats at the animal shelter is 4:1. If there are a total of 85 dogs and cats
at the shelter, how many dogs are at the shelter?

Answers

Answer:

Step-by-step explanation:

The ratio of dogs to cats is

quantities relative to each other. There are two cats and one dog. This means there are twice as many cats as dogs, or half as many dogs as cats.

...

Equivalence.

cats : dogs

8 : 4

Answer:

d

Step-by-step explanation:

yes

The model below is shaded to represent 7 3/10

Answers

Answer:

blue 7.3

Step-by-step explanation:

Answer:

7.3

Step-by-step explanation:

There are 7 groups with 10 parts in each, 7 complete rows are filled in. 3 are left in the last row. This means that there are 7 wholes with 3 left over. 7.3

if you guess what 81 ➗ 918 =
ill give brainiest

Answers

Answer:

918 ➗ 81

Step-by-step explanation:

Answer:

It's about 0.088.

if x is subtracted from 5 and the result is greater than 15. Find the range of values of x

Answers

Answer:

x<-10

Step-by-step explanation:

You can write this inequality:

5-x>15

Solving it:

5-x>15

-x>10

x<-10

I have a big question what is 720 x 0.1

Answers

Answer:

72

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

I hope this helps :)

If 11 times a number is added to twice the number, the result is 78.

Answers

The answer is 6. 6*11=66. 6*2=12. 12+66=78.

Answer:

x = 6

Step-by-step explanation:

Plsss help I suck at math and I’m sure one of you are super smart ‍♀️

Answers

Answer:

3

Step-by-step explanation:

-14x  - 7 + 5y - x = -14x - x - 7 + 5y

                         = -15x - 7 + 5y

Answer:

Step-by-step explanation:

3

Sketch the graph of y=4x2^+32x+15 using your graphing calculator. What are the x intercepts of this graph?

Answers

Answer:

x= -15/2 or -7.5

x= -1/2 or -0.5

Step-by-step explanation:

please make me brainliest

Answer:

Not C

Step-by-step explanation:

wrong

find the product (a + 3)(a - 2)

Answers

Answer:

a2 + a − 6

Step-by-step explanation:

the a with the 2 beside of it is to the power of


Jack is going to make treat bags to hand out on
Halloween. He is going to put a variety of candy in each
bag. To make 4 treat bags he will need 24 candies. How
many candies will he need to make 10 treat bags?

Answers

Answer:

60 candies

Step-by-step explanation:

60 candies will be needed to make 10 treat bags;)

Explanation:
Since there are 24 candies for 4 treat bags, you divide the amount of candies into the 4 bags. This gives you 6 candies per bag. Multiply 6 by 10(number of treat bags) to get 60.;)

PLEASE PLEASE HELP ASAP 30 POINTS AND WILL GIVE BRAINIEST

what is the measure of angle ABC
What is the measure of angle CBE
what is the measure of angle DBE
What is the measure of angle ABD​

Answers

Answer:

hope this is what u want

and don't mind my handwriting I wrote it as fast as I could

What is the purpose of having like terms on each side
of the equation?

Answers

Answer:

A frequently-used procedure in algebra is the process of combining like terms. This is a way to "clean-up" an equation and make it much easier to solve. In case you've forgotten, a term is each single part of an expression. For example, in the expression 4x+3+7y 4 x + 3 + 7 y , there are three terms: 4x , 3 , and 7y .

Can anyone help me pweeezzzz

Answers

Answer:

17

Step-by-step explanation:

ABC, which is 9z - 1, and CBD, which is 6z + 58, make up ABD, which is a total of 87 degrees.

in order to find the measurement of ABC, you first need to solve for z.

since ABC and CBD make up ABD, add those measurements and set them equal to 87, which is the measure of ABD.

9z - 1 + 6z + 58 = 87

combine like terms starting with the z terms. (it doesn't matter which like terms you combine first)

9z - 1 + 6z + 58 = 87 ⇒ 15z - 1 + 58 = 87

combine the next set of like terms.

15z - 1 + 58 = 87 ⇒ 15z + 57 = 87

subtract 57 from both sides of the equation. it'll cancel itself out on the left, leaving you with 15z = 30 after subtracting 57 from 87.

divide both sides of the equation by 15.

15z/15 = 30/15z = 2

now, plug in 2 for z in each of your equations for the measurements of ABC and CBD.

ABC = 9z - 1 ⇒ 9(2) - 1 ⇒ 18 - 1 ⇒ 17

CBD = 6z + 58 ⇒ 6(2) + 58 ⇒ 12 + 58 ⇒ 70

now, your measurements are

ABD: 87

ABC: 17

CBD: 70

check your work by adding the measurements of ABC and CBD and setting them equal to ABD, or 87.

17 + 70 = 87

87 = 87

since both sides of the equation are equal to 87, you know that your measurements are correct.

therefore, the measure of ABC is 17 degrees.

Research has shown that approximately 1 woman in 600 carries a mutation of a particular gene. About66 ​% of women with this mutation develop cancer. Find the probability that a randomly selected woman will carry the mutation of this gene and will develop cancer.

Answers

Answer:

add otherwise I don't know sorry im on that question

Step-by-step explanation:

Can someone please help me with continuity? I would like to check my work, I’m a bit confused on the differentiability part

Answers

For f to be continuous at some point x = c, you require that

f(c) exists and is finite, and

• the limits of f as x approaches c from either side match, and their value must be f(c)

For f to be differentiable at x = c, you require that

f is continuous at c (i.e. the above conditions are all met), and

• the derivative f ' is continuous at c

Without having the graph of f ', you can assess whether the last condition is met by some function by mentally tracing a tangent line to the graph as you get closer to c. If the slope of the tangent doesn't change, then the function is differentiable. This is usually accompanied by jumps or sharp corners in the graph.

Some examples:

• every polynomial is both continuous and differentiable

• the absolute value function |x| is continuous but not differentiable at x = 0

• 1/x is neither continuous nor differentiable at x = 0

(a) Neither continuous nor differentiable

Why? f has a vertical asymptote at x = -2 and f (-2) does not exist. f is not continuous, and therefore not differentiable.

(b) Neither continuous nor differentiable

Why? From the left, f is approaching 2.5, while from the right, it's approaching 5.

(c) Neither continuous nor differentiable

Why? The limits from either side of x = 2 match and are equal to 0.5, but f (2) itself does not exist (which is indicated by the point being a hollow circle).

If the circle was instead filled in, so that f (2) = 0.5, then f would be continuous there, but still not differentiable. Notice the sharp corner. Or, using the tangent-line analysis, the slope of the tangent to the left of x = 2 is negative, but to the right it would be positive.

(d) Both continuous and differentiable

Why? f doesn't have any special features at x = 3 that would suggest it's not continuous nor differentiable.

(e) Neither continuous nor differentiable

Why? Similar reasoning as in (a). There's another vertical asymptote, but the graph shows f (4) = 1. However, the limits from either side of x = 4 are positive infinity, not 1.

Find the missing side. Round
to the nearest tenth.
Х
141
43°
у
X=[?]

Answers

Answer:

x = 206.7

Step-by-step explanation:

law of sines:

sin 90° / x = sin 43° / 141

sin 43° · x = 141

x = 141 / sin 43°

The measure of the length of the hypotenuse is 206.75 and the measure of the length of the base is 151.20 units.

What is a right-angle triangle?

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

The perpendicular is 141 and the angle opposite to the perpendicular is 43 degrees. Then the value of the base and hypotenuse will be

The length of the base will be

[tex]\rm \dfrac{141}{y} = \tan 43^o\\\\y\ \ \ = \dfrac{141}{ \tan 43^o}\\\\y \ \ \ = 151.20[/tex]

Then the length of the hypotenuse will be

[tex]\rm x = \dfrac{141}{\sin 43^o}\\\\x = 206.75[/tex]

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177

#SPJ2

Please write these in a fraction form, thank you have an AMAZING day!

1. 2/5 ÷ 1/3= ?
2. 3/4 ÷ 1/2= ?​

Answers

Answer:

1 = 1 1/5

2=1 1/2

Step-by-step explanation:

If the cost of 10 tables is $750. Find the number of tables that can be purchased with $8250.

Answers

Your answer is 110. You take 10 and divide it by 750. = 75 then you take 75. Divided 8250. = 110

f(x) = x? – x3
Select the value of f(-2)
4
-12
12
A
B
C D

Answers

Step-by-step explanation:

f(x) = x² - x³

f(-2) = (-2)² - (-2)³

= 4 - (-8)

= 4 + 8 = 12

Find the y intercept and x intercept of the line below.

Answers

X intercept is 4

Y intercept is -2

Hope this helps

HELP HELPOPPPP-EWOPW0E HELP PLSSSSS

Answers

Answer:

6 more girls than boys

Step-by-step explanation:

5 out of 12 are boys  (multiply both sides of equation by 3 because 3x12 = 36)

7 out of 12 are girls   (multiply both sides of equation by 3 because 3x12 = 36)

so: 15 out of 36 are boys

so: 21 out of 36 are girls

21-15 = 6 more girls than boys

Answer: There are 6 more girls than boys

Step-by-step explanation:

To find how many more girls there are we need to find what one block equals to.

We use this equation to find it.

36 = ( 5 + 7 )x

36 = 12x

3 = x

or

x = 3 (same thing)

So each block represents 3 girls/boys

The girls have 2 more meaning there are 6 more girls than boys.

If m∠4 = 101.9°, find each of the following in degrees.
(a) m∠5
(b) m∠8

Answers

Answer:

m<5=101.9    m<8=101.9

Step-by-step explanation:

alternate interior and vertical angles

Answer:

(a) m∠5=<4[alternate angle]=101.9°,

(b) m∠8=<5[vertically opposite angle]=101.9°,

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