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
Alisiya [41]
3 years ago
14

g An urn contains 150 white balls and 50 black balls. Four balls are drawn at random one at a time. Determine the probability th

at there are 2 black balls and 2 white balls in the sample if .50 Each ball is replaced before the next one is drawn (sampling with replacement). .624 Each ball is not replaced (sampling without replacement)
Mathematics
1 answer:
xxTIMURxx [149]3 years ago
3 0

Answer:

With replacement, 0.2109 = 21.09% probability that there are 2 black balls and 2 white balls in the sample.

Without replacement, 0.2116 = 21.16% probability that there are 2 black balls and 2 white balls in the sample.

Step-by-step explanation:

For sampling with replacement, we use the binomial distribution. Without replacement, we use the hypergeometric distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

Sampling with replacement:

I consider a success choosing a black ball, so p = \frac{50}{150+50} = \frac{50}{200} = 0.25

We want 2 black balls and 2 white, 2 + 2 = 4, so n = 4, and we want P(X = 2).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 2) = C_{4,2}.(0.25)^{2}.(0.75)^{2} = 0.2109

With replacement, 0.2109 = 21.09% probability that there are 2 black balls and 2 white balls in the sample.

Sampling without replacement:

150 + 50 = 200 total balls, so N = 200

Sample of 4, so n = 4

50 are black, so k = 50

We want P(X = 2).

P(X = 2) = h(2,200,4,50) = \frac{C_{50,2}*C_{150,2}}{C_{200,4}} = 0.2116

Without replacement, 0.2116 = 21.16% probability that there are 2 black balls and 2 white balls in the sample.

You might be interested in
1. An AP Statistics class starts a project to estimate the average number of hours a student at their high school sleeps per nig
Aleks [24]

Answer:

(C) Sample: the 120 students surveyed. Population: the 1200 students at the high school. Parameter of interest: the average number of hours a student at this high school sleeps per night.

Step-by-step explanation:

The correct answer is (C). The sample is a subset of the population, and the parameter is a characteristic of the population of interest.

6 0
3 years ago
Which of the following is known as a simpler form of Euclid's fifth postulate
Deffense [45]

Answer:

A.  Playfair's axiom.

Step-by-step explanation:

In a plane, given a line and a point not on it, at most,  one line parallel to the given line can be drawn through the point.

- this implies Euclid's fifth postulate.

8 0
2 years ago
What is the area of triangle AED?
Ber [7]

Answer:

Then, the area of the right angle triangle AED is 84in^2.

Step-by-step explanation:

The triangle AED is a right angle triangle

And the area of a triangle is given as

Area=1/2base ×height

The base is 14in

And the height is 12in

Then,

Area=1/2base ×height

Area = 1/2 ×14 ×12

Area = 84in^2

Then, the area of the right angle triangle AED is 84in^2.

8 0
3 years ago
Read 2 more answers
It costs $x for a round-trip bus ticket to the mall. You have $24. Select an inequality that represents how much money you can s
lorasvet [3.4K]

Answer:you have to make the inequality first

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Find the median. 90, 88, 100, 82, 80.
gavmur [86]

Answer:

100 is the median for te above observations

<h2><em><u>HOPE</u></em><em><u> </u></em><em><u>IT</u></em><em><u> </u></em><em><u>HELPED</u></em><em><u> </u></em></h2>

3 0
3 years ago
Read 2 more answers
Other questions:
  • Alex wants to paint one side of his skateboard ramp with glow-in-the-dark paint, but he needs to know how much area he is painti
    5·1 answer
  • What x-value makes the set of ratios equivalent?
    12·1 answer
  • If my diameter is 20.6ft how would i get my radius,area,circumference?
    8·2 answers
  • Let a be directly proportional to m and n^2, and inversely proportional to y^3. If a=4 when m=9, n=4, and y=2, find a when m=7,
    6·1 answer
  • Explain how you can be<br> sure that Pro)<br> O50
    6·1 answer
  • Select the correct answer.<br> Which sequence is not equivalent to the others?
    15·2 answers
  • Use the distributive property to find the value of x.
    9·1 answer
  • What is the solution to the equation fraction 4 over 5 n minus fraction 3 over 5 equals fraction 1 over 5 n?
    10·2 answers
  • Find the length of a side of a square if its area is:<br> 0.49 square units
    7·1 answer
  • The amount of a pollutant (measured as parts per million) in a local lake can be modeled by the function of A(t)=14(2.71)^-.016*
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!