1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
omeli [17]
2 years ago
15

If we sample from a small finite population without​ replacement, the binomial distribution should not be used because the event

s are not independent. If sampling is done without replacement and the outcomes belong to one of two​ types, we can use the hypergeometric distribution. If a population has A objects of one​ type, while the remaining B objects are of the other​ type, and if n objects are sampled without​ replacement, then the probability of getting x objects of type A and nminusx objects of type B under the hypergeometric distribution is given by the following formula. In a lottery​ game, a bettor selects six numbers from 1 to 56 ​(without repetition), and a winning six​-number combination is later randomly selected. Find the probabilities of getting exactly four winning numbers with one ticket.​ (Hint: Use Aequals6​, Bequals50​, nequals6​, and xequals4​.)
Mathematics
1 answer:
seropon [69]2 years ago
6 0

Answer:

5/4324 = 0.001156337

Step-by-step explanation:

To better understand the hyper-geometric distribution consider the following example:

There are 100 senators in the US Congress, and suppose 60 of them are republicans  so 100 - 60 = 40 are democrats).

We extract a random sample of 30 senators and we want to answer this question:

What is the probability that 10 senators in the sample are republicans (and of course, 30 - 10 = 20 democrats)?

The answer using the h-g distribution is:

\large \frac{\binom{60}{10}\binom{100-60}{30-10}}{\binom{100}{30}}=\frac{\binom{60}{10}\binom{40}{20}}{\binom{100}{30}}

Now, imagine there are 56 senators (56 lottery numbers), 6 are republicans (6 winning numbers and 50 losers), we extract a sample of 6 senators (the bettor selects 6 numbers). What is the probability that 4 senators are republicans? (What is the probability that 4 numbers are winners?).

<em>As we see, the situation is exactly the same,</em> but changing the numbers. So the answer would be

\large \frac{\binom{6}{4}\binom{56-6}{6-4}}{\binom{56}{6}}=\frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}

Now compute each combination separately:

\large \binom{6}{4}=\frac{6!}{4!2!}=15\\\\\binom{50}{2}=\frac{50!}{2!48!}=1225\\\\\binom{50}{6}=\frac{50!}{6!44!}=15890700

and now replace the values:

\large \frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}=\frac{15*1225}{15890700}=\frac{18375}{15890700}=\frac{5}{4324}

and that is it.

If the decimal expression is preferred then divide the fractions to get 0.001156337

You might be interested in
Order the fractions from least to greatest: 2/3,5/6,29/36,8/9. Briefly explain your method.
elena-14-01-66 [18.8K]

Answer: 2/3, 29/36, 5/6, 8/9

Step-by-step explanation:

You find the common denominator you could use for all fractions. In this instance, you can use 36 for the common denominator.

2/3: 36/3=12, 2x12=24 therefore 2/3 becomes 24/36.

29/36: you leave this one alone, it has already been simplified.

5/6: 36/6=6, 6x5=30 therefore 5/6 becomes 30/36.

8/9: 36/9=4, 8x4=32 therefore 8/9 becomes 32/26.

4 0
2 years ago
13. Solve the system of equation using substitution.<br> 5x – 2y = 33<br> y = 7x – 39
mojhsa [17]

Answer:

The correct answer is x=5

4 0
1 year ago
Number 4 I have no idea how to do.
natta225 [31]

Volume is a three-dimensional scalar quantity. The cost of the glass is $1312.24.

<h3>What is volume?</h3>

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Given the colony must be able to take a volume of 200,000 cubic meters, therefore, the diameter of the hemisphere will be,

The volume of Hemisphere = (2/3)πr³

200,000 = (2/3) × π × R³

R = 45.7

The area of the base of the hemisphere is,

Area of the base = πR² = π×(45.7)  = 6561.185 meters²

Given the cost of glass is $0.20 per square meter, therefore, the cost of the glass of the base will be,

Cost of glass = 6561.185 × 0.20 = $1312.24

Hence, the cost of the glass is $1312.24.

Learn more about Volume:

brainly.com/question/13338592

#SPJ1

3 0
2 years ago
X-4[x-2(x+6)]=5x+3<br><img src="https://tex.z-dn.net/?f=x%20-%204%20%20%20%5B%20%20x%20-%202%28x%20%2B%206%29%5D%20%20%3D%205x%2
pshichka [43]

The equivalence of the equation is 5x + 48 = 5x + 3.

Since 48 cannot be equal to 3, hence there are no solution.

<h3>What is the value of x?</h3>

Given the equation; x-4[ x - 2( x + 6) ] = 5x + 3

We remove the parentheses

x-4[ x - 2( x + 6) ] = 5x + 3

x-4[ x - 2x - 12 ] = 5x + 3

x - 4x + 8x + 48 = 5x + 3

5x + 48 = 5x + 3

We can go further and collect like terms

5x - 5x + 48 = 3

48 ≠ 3

Since 48 cannot be equal to 3, hence there are no solution.

Learn more about equations here: brainly.com/question/14686792

#SPJ1

7 0
2 years ago
How do i solve the equation 5n+4=-26  
ozzi
You do 

-26
-4
---
-30

5n=-30 so...

-30/5=-6

Therefore 
n=-6
3 0
3 years ago
Read 2 more answers
Other questions:
  • 1 3/5 / 5/8 find the quotient.
    7·2 answers
  • Rise is the horizontal change between any two points on the line true or false
    11·2 answers
  • ann is grouping 38 rocks she can put them into groups of 10 rocks or as single rocks what are the differnet ways ann can group t
    6·1 answer
  • Plz help me and explain the answer
    5·2 answers
  • The length between any two consecutive bases of a baseball diamond is 90 feet. how much shorter is it for the catcher to walk al
    14·1 answer
  • Can someone help plzz
    15·1 answer
  • A rectangle is removed from a right triangle to create the shaded region shown below. Find the area of the shaded region. Be sur
    9·1 answer
  • HELP please lol ill love u forever if u do this for me bestie
    7·1 answer
  • Evaluate: x(y – 5) for x = 2 and y = 7
    11·1 answer
  • which equation represents a proportional relationship that has a constant of proportionality equal to ?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!