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faltersainse [42]
3 years ago
15

Estimate. then ,divide using the standard algorithm and check 45.15/21

Mathematics
1 answer:
insens350 [35]3 years ago
7 0
I estimated to 45 then divided 21 and got about 2.1


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Consider an experiment that consists of recording the birthday for each of 20 randomly selected persons. Ignoring leap years, we
8_murik_8 [283]

Answer:

a)  p_{20d} = 0.588

b) 23

c) 47

Step-by-step explanation:

To find a solution for this question we must consider the following:

If we’d like to know the probability of two or more people having the same birthday we can start by analyzing the cases with 1, 2 and 3 people

For n=1 we only have 1 person, so the probability  p_{1} of sharing a birthday is 0 (p_{1}=0)

For n=2 the probability p_{2} can be calculated according to Laplace’s rule. That is, 365 different ways that a person’s birthday coincides, one for every day of the year (favorable result) and 365*365 different ways for the result to happen (possible results), therefore,

p_{2} = \frac{365}{365^{2} } = \frac{1}{365}

For n=3 we may calculate the probability p_{3} that at least two of them share their birthday by using the opposite probability P(A)=1-P(B). That means calculating the probability that all three were born on different days using the probability of the intersection of two events, we have:

p_{3} = 1 - \frac{364}{365}*\frac{363}{365} = 1 - \frac{364*363}{365^{2} }

So, the second person’s birthday might be on any of the 365 days of the year, but it won’t coincide with the first person on 364 days, same for the third person compared with the first and second person (363).

Let’s make it general for every n:

p_{n} = 1 - \frac{364}{365}*\frac{363}{365}*\frac{362}{365}*...*\frac{(365-n+1)}{365}

p_{n} = \frac{364*363*362*...*(365-n+1)}{365^{n-1} }

p_{n} = \frac{365*364*363*...*(365-n+1)}{365^{n} }

p_{n} = \frac{365!}{365^{n}*(365-n)! }

Now, let’s answer the questions!

a) Remember we just calculated the probability for n people having the same birthday by calculating 1 <em>minus the opposite</em>, hence <em>we just need the second part of the first calculation for</em> p_{n}, that is:

p_{20d} = \frac{364}{365}*\frac{363}{365}*\frac{362}{365}*...*\frac{(365-20+1)}{365}

We replace n=20 and we obtain (you’ll need some excel here, try calculating first the quotients then the products):

p_{20d} = 0.588

So, we have a 58% probability that 20 people chosen randomly have different birthdays.

b) and c) Again, remember all the reasoning above, we actually have the answer in the last calculation for pn:

p_{n} = \frac{365!}{365^{n}*(365-n)! }

But here we have to apply some trial and error for 0.50 and 0.95, therefore, use a calculator or Excel to make the calculations replacing n until you find the right n for p_{n}=0.50 and p_{n}=0.95

b) 0.50 = 365!/(365^n)*(365-n)!

n           p_{n}

1              0

2           0,003

3           0,008

….           …

20           0,411

21           0,444

22           0,476

23           0,507

The minimum number of people such that the probability of two or more of them have the same birthday is at least 50% is 23.

c) 0.95 = 365!/(365^n)*(365-n)!

We keep on going with the calculations made for a)

n             p_{n}

…                …

43            0,924

44            0,933

45            0,941

46            0,948

47            0,955

The minimum number of people such that the probability of two or more of them have the same birthday is at least 95% is 47.

And we’re done :)

6 0
3 years ago
Which of these strategies would eliminate a variable in the system of equations?
Novay_Z [31]

Answer:

A.

Step-by-step explanation:

multiply the to equation by 6, multiply the bottom equation by -5 (you will get +30y and -30y to eliminate each other)then add equations (you will have +48x and +45x which will be = -42 + 20)

4 0
3 years ago
Read 2 more answers
A hair stylist offers haircuts and hair coloring to his customers. A haircut costs $18 and hair coloring costs $42. Yesterday, t
TEA [102]

Answer:

haircut =9 and hair color= 3

Step-by-step explanation:

Step one:

GIven data

let the haircut be x

and hair color be y in numbers.

so

18x+42y=288------------1

x+y=12---------------------2

from 1

x=12-y, put this in 2, we have

18(12-y)+42y=288

216-18y+42y=288

collect like terms

24y=288-216

24y=72

divide both sides by 24

y=72/24

y=3

put y= 3 in 2

x+3= 12

x= 12-3

x=9

4 0
2 years ago
Please help and explain
BARSIC [14]
1. 8y-7 is one way. Hope that helped!:)
7 0
3 years ago
<img src="https://tex.z-dn.net/?f=%5Csf%20what%27s%5C%3A%20the%20%5C%3Aanswer%5C%3A%3F" id="TexFormula1" title="\sf what's\: the
daser333 [38]

Answer:

x = 10

Explanation:

4(x) + 3(x-1) = 67

<u>apply distributive method</u>

  • 4(x) + 3(x) -3(1) = 67

<u>simplify</u>

  • 7(x) - 3 = 67

<u>change side</u>

  • 7(x) = 67 + 3

<u>simplify</u>

  • 7(x) = 70

<u>divide both sides by 7</u>

  • x = 10
5 0
2 years ago
Read 2 more answers
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