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
beks73 [17]
2 years ago
6

In a string of 12 Christmas tree light bulbs, 3 are defective. The bulbs are selected at random and tested, one at a time, until

the third defective bulb is found. Compute the probability that the third defective bulb is the fifth bulb tested.
Mathematics
1 answer:
Juliette [100K]2 years ago
8 0

Using the hypergeometric distribution, it is found that there is a 0.0273 = 2.73% probability that the third defective bulb is the fifth bulb tested.

In this problem, the bulbs are chosen without replacement, hence the <em>hypergeometric distribution</em> is used to solve this question.

<h3>What is the hypergeometric distribution formula?</h3>

The formula is:

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

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

The parameters are:

  • x is the number of successes.
  • N is the size of the population.
  • n is the size of the sample.
  • k is the total number of desired outcomes.

In this problem:

  • There are 12 bulbs, hence N = 12.
  • 3 are defective, hence k = 3.

The third defective bulb is the fifth bulb if:

  • Two of the first 4 bulbs are defective, which is P(X = 2) when n = 4.
  • The fifth is defective, with probability of 1/8, as of the eight remaining bulbs, one will be defective.

Hence:

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

P(X = 2) = h(2,12,4,3) = \frac{C_{3,2}C_{9,1}}{C_{12,4}} = 0.2182

0.2182 x 1/8 = 0.0273.

0.0273 = 2.73% probability that the third defective bulb is the fifth bulb tested.

More can be learned about the hypergeometric distribution at brainly.com/question/24826394

You might be interested in
How do you identify the opposite and the absolute value of a rational number
Sergeeva-Olga [200]

Rational numbers are the numbers that can be written as the fraction of two integers and absolute value is the distance a number is away from 0. If we look at a number line, the absolute value is the distance any number on the number line is away from 0. Distance is always positive, so our absolute value is always 0.

8 0
3 years ago
Simplify 3^8 x 3^4 / 3^2 x 3^8 leaving your answer in index form
Furkat [3]

Answer:

3² or 9

Step-by-step explanation:

Step 1: Add exponents

\frac{3^{12}}{3^{10}}

Step 2: Subtract exponents

You should get 3² because of exponent rules. Remember when you multiply exponents you add the powers and when you divide exponents you subtract the powers.

3 0
2 years ago
Read 2 more answers
At an amusement park, a group of 154 people wants to ride the roller coaster. If each car on the roller coaster holds 9 people,
Vsevolod [243]

Answer:

1

Step-by-step explanation:

you simply divide 154 by 9, get around 17.1. 17 is the closest whole number answer, so 17*9 is 153.

do 154-153, you get 1.

not the best explaination but i hope it helps.

6 0
3 years ago
When 2/3 is added to a certain number, the sum is 3 greater than twice the number. part 1: set up an equation using n to represe
Gennadij [26K]
2/3 + n = 2n + 3 <== ur equation
2/3 - 3 = 2n - n
2/3 - 9/3 = n
-7/3 = n <== ur solution

or
2/3 + n = 2n + 3...multiply everything by common denominator of 3
2 + 3n = 6n + 9
2 - 9 = 6n - 3n
-7 = 3n
-7/3 = n
7 0
2 years ago
Your friend has prepared his mountly budget and asks you if he has overlooked anything in this planning. Which of the following
cluponka [151]
The answer is " what if the electric bill increases?"
3 0
3 years ago
Other questions:
  • What is 552945 rounded to one hundred thousands
    13·1 answer
  • How to estimate 586-321 two different ways
    11·1 answer
  • A notebook costs $6.50 plus sales tax. After sales tax, the notebook is $6.89. What is the sales tax rate?
    14·2 answers
  • Determine whether the given equation has one solution, no solution, or infinitely many solutions.
    5·2 answers
  • Plz help Name the polygon that has five sides: quadrilateral octagon pentagon
    14·2 answers
  • Quincy wants to go to the movies with his friends
    11·2 answers
  • Which measurement is equivalent to 5 quarts?
    14·1 answer
  • Is the square root of any positive number irrational
    5·1 answer
  • A cylindrical soup can has a radius of 1.5 in. and is 4.7 in. tall. Find the volume of the can.
    9·1 answer
  • What’s an irrational number between 5.2 and 5.5
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!