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
Leona [35]
3 years ago
11

Two machines turn out all the products in a factory, with the first machine producing 40%of the product and the second 60%. The

first machine produces defective products 2% of the timeand the second machine 4% of the time. Given a defective product, what is the probability it wasproduced on the first machine
Mathematics
2 answers:
Mice21 [21]3 years ago
7 0

Answer:

Given a defective product, the probability it was produced on the first machine is \\ P(F|D) = 0.25.

Step-by-step explanation:

This is a case that can be solved using the <em>Bayes' Theorem</em>, which implies <em>conditional probabilities</em>.

We have to remember that in conditional probabilities, the <em>sample space</em> is replaced by the probability of a given event (as can be seen below).

First, we need to find the probability of <em>producing a defective product</em>:

\\ P(D) = P(D|F)*P(F) + P(D|S)*P(S) (1)

Where

P(D), the probability of producing a <em>defective product</em>.

P(F), the probability that the product was <em>produced by the first machine</em>. In this case, P(F) = 0.40.

P(S), the probability that the product was produced <em>by the second machine</em>. In this case, P(S) = 0.60.

P(D|F), a conditional probability that the product is <em>defective</em> given (or assuming) that it was produced by the <em>first machine</em>. In this case, from the question, P(D|F) = 0.02.

P(D|S), a conditional probability that the product is <em>defective</em> given (or assuming) that it was produced by the <em>second machine</em>. In this case, from the question, P(D|S) = 0.04.

So, from formula (1):

\\ P(D) = P(D|F)*P(F) + P(D|S)*P(S)

\\ P(D) = 0.02*0.40 + 0.04*0.60

\\ P(D) = 0.032

That is, the probability of producing a defective product from these two machines is P(D) = 0.032.

From conditional probabilities we know that:

\\ P(A \cap B) = P(A|B)*P(B)

\\ P(A \cap B) = P(B|A)*P(A) = P(B \cap A)

So

\\ P(A|B)*P(B) = P(B|A)*P(A)

In the same way, we can say that

\\ P(F|D)*P(D) = P(D|F)*P(F) = P(D \cap F) = P(F \cap D)

In words, the probability that both events (D and F) occur is given by the "relationship" of conditional probabilities between these two events.

Then

The probability that a product comes from the first machine, given it is  defective is as follows:

\\ P(F|D)*P(D) = P(D|F)*P(F)

\\ P(F|D) = \frac{P(D|F)*P(F)}{P(D)}

\\ P(F|D) = \frac{0.02*0.40}{0.032}

\\ P(F|D) = 0.25 or 25%.

vovikov84 [41]3 years ago
5 0

Answer:

0.4

Step-by-step explanation:

First Machine(M1) Produces 40% of the product.

P(M1)=40%=0.4

The first Machine Produces defective product(D) 2% of the Time.

P(D)=2%=0.02

Given a defective product(D), we want to find the probability that it was produced on the first machine(M1).

P(M1|D)=P(M1∩D)/P(D)

=(0.4 X 0.02)/0.02

=0.4

You might be interested in
The scatter plot shows the maximum noise level when different numbers of the people are in the stadium. The linear model is give
Sholpan [36]
The y intercept is 1.5x+22.7 + the linear equation which is 22
8 0
2 years ago
Can someone answer my newest question please will give brainly
Aleksandr-060686 [28]

Answer:

yes if you give me brainliest

Step-by-step explanation:

8 0
2 years ago
Kareem cannot decide which of two washing machines to buy. The selling price of each
Makovka662 [10]

Answer:

k

Step-by-step explanation:

give me a minute

7 0
3 years ago
Select all of the equations that are not functions.
Kryger [21]

Answer:

B

Step-by-step explanation:

x² + y² = 3  creates a circle and circles are not functions because one x-value relates to two y-values instead of one

7 0
2 years ago
Ishaan is 222 times as old as Christopher. 353535 years ago, Ishaan was 777 times as old as Christopher.
klemol [59]
<h3><u>Question:</u></h3>

Ishaan is 2 times as old as Christopher. 35 years ago, Ishaan was 7 times as old as Christopher. How old is Christoper now?

<h3><u>Answer:</u></h3>

The present age of Christoper is 42 years old

<h3><u>Solution:</u></h3>

Given that Ishaan is 2 times as old as Christoper

Let the present age of Christoper be "x"

Then, Present age of Ishaan = 2 times as old as Christoper

present age of Ishaan = 2x

<em><u>35 years ago, Ishaan was 7 times as old as Christopher</u></em>

Age of Ishaan 35 years ago = Present age of Ishaan - 35

Age of Ishaan 35 years ago = 2x - 35

Similarly,

Age of christoper 35 years ago = Present age of christoper - 35

Age of christoper 35 years ago = x - 35

From given statement, 35 years ago, Ishaan was 7 times as old as Christopher

Age of Ishaan 35 years ago = 7 times the age of Christoper 35 years ago

(2x - 35) = 7(x - 35)

<em><u>Solve the above equation for "x"</u></em>

2x - 35 = 7x - 245

2x - 7x = -245 + 35

-5x = -210

<h3>x = 42</h3>

Thus present age of Christoper is 42 years old

5 0
3 years ago
Other questions:
  • What is the percentage of sugar in the syrup made of 10 kg of water and 5 kg of sugar?
    6·1 answer
  • Multiple choice help please!!!!
    13·2 answers
  • Sam ate a total of 13 hotdogs. He ate 2 hotdogs every 4 minutes. How many minutes did it take for Sam to finish all 13 hotdogs?
    13·1 answer
  • What is 119.63 rounded to the nearest whole number ?
    10·2 answers
  • PLEASE HELP ALGEBRA QUESTION ​
    14·1 answer
  • Give the function w(x)=9×+8, evaluate w(5)
    11·1 answer
  • Is 1/6 or 1/7 larger
    9·2 answers
  • kenya is reserving a room in a hotel in france where they use euros the room charge is 75 euros .suppose the conversation rate i
    9·1 answer
  • Compare 1/2 with 3/4 using &lt; &gt; =?
    12·2 answers
  • The coordinates of the vertices of △DEF are D (1, 2) , E (2, 0) , and F (−1, 0) .
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!