# Probability problem.

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This discussion is closed.
17 years ago
#1
A manufactured component is checked by two inspectors to see whether it is defective or not. A
examines 35% and B the remainder. A misses 7% and B 10% of defective items and both will pass 95% of
good components. If 10% of the output is defective what is the probability that a component that is
passed is indeed a good component?

Just need an answer to check against my own. Thanks
0
17 years ago
#2
In article <[email protected] sting.google.com>, Deathstar
<[email protected]> wrote:
[q1]>A manufactured component is checked by two inspectors to see whether it is defective or not. A[/q1]
[q1]>examines 35% and B the remainder. A misses 7% and B 10% of defective items and both will pass 95%[/q1]
[q1]>of good components. If 10% of the output is defective what is the probability that a component that[/q1]
[q1]>is passed is indeed a good component?[/q1]
[q1]>[/q1]
[q1]>Just need an answer to check against my own.[/q1]

You have more chance if you post your own. Then none of us nasty, suspicious types will suspect you
of skullduggery.

--
Rob. http://www.mis.coventry.ac.uk/~mtx014/
0
17 years ago
#3
[email protected] (Deathstar) wrote in message
news:<bfa9eb20.0205170354.53b878 [email protected]>...
[q1]> A manufactured component is checked by two inspectors to see whether it is defective or not. A[/q1]
[q1]> examines 35% and B the remainder. A misses 7% and B 10% of defective items and both will pass 95%[/q1]
[q1]> of good components. If 10% of the output is defective what is the probability that a component[/q1]
[q1]> that is passed is indeed a good component?[/q1]
[q1]>[/q1]
[q1]> Just need an answer to check against my own. Thanks[/q1]

Sorry! The answer I got was .7998. This just does not seem right, Newton I ain't.
0
17 years ago
#4
[email protected] (Deathstar) wrote:

[q1]>A manufactured component is checked by two inspectors to see whether it is defective or not. A[/q1]
[q1]>examines 35% and B the remainder. A misses 7% and B 10% of defective items and both will pass 95%[/q1]
[q1]>of good components. If 10% of the output is defective what is the probability that a component that[/q1]
[q1]>is passed is indeed a good component?[/q1]
[q1]>[/q1]
[q1]>Just need an answer to check against my own.[/q1]

What is your answer? I'll tell you if it is right or not.

Gareth
0
17 years ago
#5
Deathstar <[email protected]> wrote in uk.education.maths:
[q1]>Just need an answer to check against my own.[/q1]

0
17 years ago
#6
"Deathstar" <[email protected]> wrote in message
news:[email protected]...
[q1]> [email protected] (Deathstar) wrote in message[/q1]
news:<bfa9eb20.0205170354.53b878 [email protected]>...
[q2]> > A manufactured component is checked by two inspectors to see whether it is defective or not. A[/q2]
[q2]> > examines 35% and B the remainder. A misses 7% and B 10% of defective items and both will pass[/q2]
[q2]> > 95% of good components. If 10% of the output is defective what is the probability that a[/q2]
[q2]> > component that is passed is indeed a good component?[/q2]
[q2]> >[/q2]
[q2]> > Just need an answer to check against my own. Thanks[/q2]
[q1]>[/q1]
[q1]> Sorry! The answer I got was .7998. This just does not seem right, Newton I[/q1]
ain't.

Seeing just the answer would not help much, and logic would indicate that if 90% output is good
anyway, and you try to filter out the bad from that lot, you should not end up with a worse
situation. Perhaps you can share your approach so that we can find where it went off track?

regards.
0
17 years ago
#7
"Rino Raj" <[email protected]> wrote in message news:<[email protected]>...
[q1]> "Deathstar" <[email protected]> wrote in message[/q1]
[q1]> news:[email protected]...[/q1]
[q2]> > [email protected] (Deathstar) wrote in message[/q2]
[q1]> news:<bfa9eb20.0205170354.53b878 [email protected]>...[/q1]
[q3]> > > A manufactured component is checked by two inspectors to see whether it is defective or not. A[/q3]
[q3]> > > examines 35% and B the remainder. A misses 7% and B 10% of defective items and both will pass[/q3]
[q3]> > > 95% of good components. If 10% of the output is defective what is the probability that a[/q3]
[q3]> > > component that is passed is indeed a good component?[/q3]
[q3]> > >[/q3]
[q3]> > > Just need an answer to check against my own. Thanks[/q3]
[q2]> >[/q2]
[q2]> > Sorry! The answer I got was .7998. This just does not seem right, Newton I[/q2]
[q1]> ain't.[/q1]
[q1]>[/q1]
[q1]> Seeing just the answer would not help much, and logic would indicate that if 90% output is good[/q1]
[q1]> anyway, and you try to filter out the bad from that lot, you should not end up with a worse[/q1]
[q1]> situation. Perhaps you can share your approach so that we can find where it went off track?[/q1]
[q1]>[/q1]
[q1]> regards.[/q1]

For F*** sake, all I wanted was the F***ing answer to the question, there is no need to be such a
nerdy usenet stuck up your own hole **** about it. It was a past examination question I needed
advice on, not the secret of everlasting life. And for your interest I thought dividing the
probabilty of the sum of all the good items that were passed, against the probability of actual good
items was the answer. But you obviously can't make a response without being 'trigger' about
it. Good for you!!!
0
17 years ago
#8
In article <[email protected] sting.google.com>, [email protected]
(Deathstar) wrote:

[q1]> "Rino Raj" <[email protected]> wrote in message news:<[email protected]>...[/q1]
[q2]> > "Deathstar" <[email protected]> wrote in message[/q2]
[q2]> > news:[email protected]...[/q2]
[q3]> > > [email protected] (Deathstar) wrote in message[/q3]
[q2]> > news:<bfa9eb20.0205170354.53b878 [email protected]>...[/q2]
[q3]> > > > A manufactured component is checked by two inspectors to see whether it is defective or not.[/q3]
[q3]> > > > A examines 35% and B the remainder. A misses 7% and B 10% of defective items and both will[/q3]
[q3]> > > > pass 95% of good components. If 10% of the output is defective what is the probability that[/q3]
[q3]> > > > a component that is passed is indeed a good component?[/q3]
[q3]> > > >[/q3]
[q3]> > > > Just need an answer to check against my own. Thanks[/q3]
[q3]> > >[/q3]
[q3]> > > Sorry! The answer I got was .7998. This just does not seem right, Newton I[/q3]
[q2]> > ain't.[/q2]
[q2]> >[/q2]
[q2]> > Seeing just the answer would not help much, and logic would indicate that if 90% output is good[/q2]
[q2]> > anyway, and you try to filter out the bad from that lot, you should not end up with a worse[/q2]
[q2]> > situation. Perhaps you can share your approach so that we can find where it went off track?[/q2]
[q2]> >[/q2]
[q2]> > regards.[/q2]
[q1]>[/q1]
[q1]>[/q1]
[q1]> For F*** sake, all I wanted was the F***ing answer to the question, there is no need to be such a[/q1]
[q1]> nerdy usenet stuck up your own hole **** about it. It was a past examination question I needed[/q1]
[q1]> advice on, not the secret of everlasting life. And for your interest I thought dividing the[/q1]
[q1]> probabilty of the sum of all the good items that were passed, against the probability of actual[/q1]
[q1]> good items was the answer. But you obviously can't make a response without being 'trigger' about[/q1]
[q1]> it. Good for you!!![/q1]

I make the correct answer to be almost 99%. I worked out this value by building a 3-level tree
diagram of probabilities to find the probabilities of each of the 8 compound outcomes possible:
{good,defective}x{InsectorA,Insp ectorB}x{passed, rejected}

Then a very little arithemtic gives the result.
0
17 years ago
#9
Deathstar <[email protected]> wrote:
[q1]>For F*** sake, all I wanted was the F***ing answer to the question, there is no need to be such a[/q1]
[q1]>nerdy usenet stuck up your own hole **** about it. It was a past examination question I needed[/q1]

Grow up. You asked a bunch of strangers what could easily have been a homework question, and were
asked to show what you had done for comment. If you want help, show that you're a responsible
student, not just looking for a free ride.

--
Rob. http://www.mis.coventry.ac.uk/~mtx014/
0
17 years ago
#10
[email protected] (Deathstar) wrote in message
news:<bfa9eb20.0205170354.53b878 [email protected]>...
[q1]> A manufactured component is checked by two inspectors to see whether it is defective or not. A[/q1]
[q1]> examines 35% and B the remainder. A misses 7% and B 10% of defective items and both will pass 95%[/q1]
[q1]> of good components. If 10% of the output is defective what is the probability that a component[/q1]
[q1]> that is passed is indeed a good component?[/q1]
[q1]>[/q1]
[q1]> Just need an answer to check against my own. Thanks[/q1]

You see I can do tree diagrams with 2 conditions, just not with three, do I start the tree diagram,
with the 10% defective, 90% good as the first condition, or do I start it with the 35%/65%
examinations.

P(P/AnD)=0.07
P(Q/BnD)=0.10
P(R/AnG)=0.05
P(S/BnG)=0.05
P(T)=.10
P(U)=.90
P(V)=.35
P(W)=.65

If I knew which condition I started the diagram with, then the rest will fall into place. Thanks.
0
17 years ago
#11
[email protected] (Deathstar) wrote:

[q1]>[email protected] (Deathstar) wrote in message[/q1]
[q1]>news:<bfa9eb20.0205170354.53b87 [email protected]>...[/q1]
[q2]>> A manufactured component is checked by two inspectors to see whether it is defective or not. A[/q2]
[q2]>> examines 35% and B the remainder. A misses 7% and B 10% of defective items and both will pass 95%[/q2]
[q2]>> of good components. If 10% of the output is defective what is the probability that a component[/q2]
[q2]>> that is passed is indeed a good component?[/q2]
[q2]>>[/q2]
[q2]>> Just need an answer to check against my own. Thanks[/q2]
[q1]>[/q1]
[q1]>You see I can do tree diagrams with 2 conditions, just not with three, do I start the tree diagram,[/q1]
[q1]>with the 10% defective, 90% good as the first condition, or do I start it with the 35%/65%[/q1]
[q1]>examinations.[/q1]
[q1]>[/q1]
[q1]>P(P/AnD)=0.07[/q1]
[q1]>P(P/BnD)=0.10[/q1]
[q1]>P(F/AnG)=0.05[/q1]
[q1]>P(F/BnG)=0.05[/q1]
[q1]>P(D)=.10[/q1]
[q1]>P(G)=.90[/q1]
[q1]>P(A)=.35[/q1]
[q1]>P(B)=.65[/q1]

You need to find P(G|P).

P(G|P) = P(GnP) / P(P)

or:

P(G|P) = P(P|G)P(G) / P(P)

You know some of these values, so:

P(G|P) = 0.95 * 0.90 / P(P) P(G|P) = 0.855 / P(P) (1)

P(P) = P(P|G)P(G) + P(P|AnD)P(AnD) + P(P|BnD)P(BnD)

which is:
P(Q) = 0.855 + P(P|AnD)P(AnD) + P(P|BnD)P(BnD)

or
P(R) = 0.855 + 0.07 * P(AnD) + 0.10 *P(BnD)

taking P(AnD):

P(AnD) = P(A|D)P(D), but A and D are independent, so P(A|D) = P(A), and:

P(AnD) = P(A)P(D) = 0.35 * .1 = 0.035

likewise P(BnD) = 0.065

so from (2)

P(S) = 0.855 + 0.07 * 0.035 + 0.10 * 0.065 = 0.86395

and from (1):

P(G|P) = 0.855 / 0.86395 P(G|P) = 0.9896

I think.

Gareth
0
17 years ago
#12
"Deathstar" <[email protected]> wrote in message
news:[email protected]...
[q1]> "Rino Raj" <[email protected]> wrote in message[/q1]
news:<[email protected]>...
[q2]> > "Deathstar" <[email protected]> wrote in message[/q2]
[q2]> > news:[email protected]...[/q2]
[q3]> > > [email protected] (Deathstar) wrote in message[/q3]
[q2]> > news:<bfa9eb20.0205170354.53b878 [email protected]>...[/q2]
[q3]> > > > A manufactured component is checked by two inspectors to see whether it is defective or not.[/q3]
[q3]> > > > A examines 35% and B the remainder. A misses 7% and B 10% of defective items and both will[/q3]
[q3]> > > > pass 95% of good components. If 10% of the output is defective what is the[/q3]
probability
[q3]> > > > that a component that is passed is indeed a good component?[/q3]
[q3]> > > >[/q3]
[q3]> > > > Just need an answer to check against my own. Thanks[/q3]
[q3]> > >[/q3]
[q3]> > > Sorry! The answer I got was .7998. This just does not seem right,[/q3]
Newton I
[q2]> > ain't.[/q2]
[q2]> >[/q2]
[q2]> > Seeing just the answer would not help much, and logic would indicate[/q2]
that if
[q2]> > 90% output is good anyway, and you try to filter out the bad from that[/q2]
lot,
[q2]> > you should not end up with a worse situation. Perhaps you can share[/q2]
your
[q2]> > approach so that we can find where it went off track?[/q2]
[q2]> >[/q2]
[q2]> > regards.[/q2]
[q1]>[/q1]
[q1]>[/q1]
[q1]> For F*** sake, all I wanted was the F***ing answer to the question, there is no need to be such a[/q1]
[q1]> nerdy usenet stuck up your own hole **** about it. It was a past examination question I needed[/q1]
[q1]> advice on, not the secret of everlasting life. And for your interest I thought dividing the[/q1]
[q1]> probabilty of the sum of all the good items that were passed, against the probability of actual[/q1]
[q1]> good items was the answer. But you obviously can't make a response without being 'trigger' about[/q1]
[q1]> it. Good for you!!![/q1]

Through all that muck, there is your approach sneaking through also. What you have worked out seems
to be the probability that a good item passes. For what you ask for, you take all the actual good
items passed and divide it by the number of items passed. Think a bit about it. Say 100 items are
the output. 90 ought to be good, and both would pass 95% of that, so that is 85.5 good ones passing.
Out of the faulty 10, 3.5 gets examined by A, and 3.5*7% passes. Similarly B passes 6.5*10% bad
ones. So you have the good ones that pass, and the total that pass.

That whole argument should be made a bit more rigorous to use. But I suppose you already know you
need to work on your presentation. LOL.
0
17 years ago
#13
Deathstar <[email protected]> wrote in uk.education.maths:
[q1]>For F*** sake, all I wanted was the F***ing answer to the question, there is no need to be such a[/q1]

And why exactly do you think we are obliged to provide it to you on your terms, without your doing
anything? Whence comes this sense of entitlement that leads you to swear at people from whom you are

Students post all the time asking for answers. But what they need is not a mere answer but to learn
how to solve the problem. The only way to give true help is to look at what the student did so we
can help him get past a "stuck place" or correct a conceptual or careless error.

--
Stan Brown, Oak Road Systems, Cortland County, New York, USA http://oakroadsystems.com/ "That was a
stupid lie, easy to expose, not worthy of you." George Sanders as "Addison Dewitt" in /All About
Eve/ (1950)
0
17 years ago
#14
Robert Low <[email protected] ac.uk> wrote in message
news:[email protected]...
[q1]>[/q1]
[q1]> Deathstar <[email protected]> wrote:[/q1]
[q2]> >For F*** sake, all I wanted was the F***ing answer to the question, there is no need to be such a[/q2]
[q2]> >nerdy usenet stuck up your own hole **** about it. It was a past examination question I needed[/q2]
[q1]>[/q1]
[q1]> Grow up. You asked a bunch of strangers what could easily have been a homework question, and were[/q1]
[q1]> asked to show what you had done for comment. If you want help, show that you're a responsible[/q1]
[q1]> student, not just looking for a free ride.[/q1]
[q1]>[/q1]

I agree that this ng shouldn't be offering "solutions" without at least confirming the student has
made a reasonable effort, but to be fair to deathstar, he specifically asked for an answer in order
to compare with his own. Answer and solution are not the same thing.

--
Martin

0
17 years ago
#15
martin <[email protected] k> wrote in uk.education.maths:
[q1]>I agree that this ng shouldn't be offering "solutions" without at least confirming the student has[/q1]
[q1]>made a reasonable effort, but to be fair to deathstar, he specifically asked for an answer in order[/q1]
[q1]>to compare with his own. Answer and solution are not the same thing.[/q1]

And "Post your answer, I just want to compare it with mine" is often code for "I just want an answer
to write on my paper; I haven't actually solved the problem and don't intend to."

--
Stan Brown, Oak Road Systems, Cortland County, New York, USA http://oakroadsystems.com/ "My theory
was a perfectly good one. The facts were misleading." -- /The Lady Vanishes/ (1938)
0
17 years ago
#16
Stan Brown <[email protected]> wrote in message news:[email protected]...
[q1]> martin <[email protected] k> wrote in uk.education.maths:[/q1]
[q2]> >I agree that this ng shouldn't be offering "solutions" without at least confirming the student[/q2]
[q2]> >has made a reasonable effort, but to be fair to deathstar, he specifically asked for an answer in[/q2]
[q2]> >order to compare with[/q2]
his
[q2]> >own. Answer and solution are not the same thing.[/q2]
[q1]>[/q1]
[q1]> And "Post your answer, I just want to compare it with mine" is often code for "I just want an[/q1]
[q1]> answer to write on my paper; I haven't actually solved the problem and don't intend to."[/q1]

I very much doubt it - at least in UK.

If any UK maths teacher was so incompetent as to mark answers without looking at solution / method,
then there is no (i.e. zero) possibility that student has been taught how to tackle / solve the
problem in the first place.

Do you mark differently across the pond? And if so, why mark at all?

--
Martin

0
17 years ago
#17
martin <[email protected] k> wrote in uk.education.maths:
[q1]>Stan Brown <[email protected]> wrote in message[/q1]
[q1]>news:[email protected]...[/q1]
[q2]>> martin <[email protected] k> wrote in uk.education.maths:[/q2]
[q2]>> >I agree that this ng shouldn't be offering "solutions" without at least confirming the student[/q2]
[q2]>> >has made a reasonable effort, but to be fair to deathstar, he specifically asked for an answer[/q2]
[q2]>> >in order to compare with his own. Answer and solution are not the same thing.[/q2]
[q2]>>[/q2]
[q2]>> And "Post your answer, I just want to compare it with mine" is often code for "I just want an[/q2]
[q2]>> answer to write on my paper; I haven't actually solved the problem and don't intend to."[/q2]
[q1]>[/q1]
[q1]>I very much doubt it - at least in UK.[/q1]
[q1]>[/q1]
[q1]>If any UK maths teacher was so incompetent as to mark answers without looking at solution / method,[/q1]
[q1]>then there is no (i.e. zero) possibility that student has been taught how to tackle / solve the[/q1]
[q1]>problem in the first place.[/q1]

I think we agree philosophically. But I commented as I did because the person posting was a student.
We teachers know that an answer is worthless without a solution, but a great many students seem not
to appreciate that. They think that the goal of working homework is to put answers on paper, not to
understand and practice solution methods. And no matter how many times we correct that impression,
it i curiously hard to eradicate.

[q1]>Do you mark differently across the pond? And if so, why mark at all?[/q1]

No, I don't mark differently. But students never stop hoping I will.
[q1]:-)[/q1]

Our textbooks usually show answers to odd-numbered problems, and I like to assign odd-numbered
problems so that students can check their own work. I used to collect homework occasionally, but I
found that perhaps a third of the class would simply copy the answers from the back of the book.
Obviously there was no learning going on there.

For that reason I have pretty much stopped collecting homework. Now I tell my students, "I don't
collect homework, because if you don't do the problems you will fail every exam."

Nevertheless there are teachers in the US (and in the UK too, I'll bet) who do mark answers and
don't check solutions. There is one teacher at my college who gives only multiple-choice questions
for homework and quizzes. Personally I find it very difficult to see what educational purpose is
being served. Perhaps one day I'll get around to asking that teacher about his educational
philosophy.

--
Stan Brown, Oak Road Systems, Cortland County, New York, USA http://oakroadsystems.com/ "What in
heaven's name brought you to Casablanca?" "My health. I came to Casablanca for the waters." "The
waters? What waters? We're in the desert." "I was misinformed."
0
17 years ago
#18
Stan Brown <[email protected]> wrote in message
news:[email protected]... <snip>

What age / level are you teaching?

I'm suprised that you don't check homework in order to identify both shared and individual problems
/ confusions. Or are you distinguishing between "checking" in class and actually collecting in for

In public exams here, nearly all the marks go for "method", and hardly any for answer. Actually
makes it tough the bright kid who can for example jump several steps in his/her head :-(

--
Martin

0
17 years ago
#19
martin <[email protected] k> wrote in uk.education.maths:
[q1]>[/q1]
[q1]>Stan Brown <[email protected]> wrote in message[/q1]
[q1]>news:[email protected]... <snip>[/q1]
[q1]>[/q1]
[q1]>What age / level are you teaching?[/q1]

Community college. I don't know whether the UK has community colleges. The two years of comm.coll.
are ideally equivalent to the first two years of university, but for many students a chunk of the
time is used to make up the deficits of secondary school.

[q1]>I'm suprised that you don't check homework in order to identify both shared and individual problems[/q1]
[q1]>/ confusions. Or are you distinguishing between "checking" in class and actually collecting in for[/q1]

Exactly. I have some class time for students to work individually or in groups (their choice), and I
circulate to answer questions and see where students are having trouble. Short "pop" (unannounced)
quizzes also give information.

[q1]>In public exams here, nearly all the marks go for "method", and hardly any for answer. Actually[/q1]
[q1]>makes it tough the bright kid who can for example jump several steps in his/her head :-([/q1]

That's an issue I've been struggling with myself. I keep preaching "show your work", but some
students really can solve sin(2x) = 1 in their heads.

--
Stan Brown, Oak Road Systems, Cortland County, New York, USA http://oakroadsystems.com/ "What in
heaven's name brought you to Casablanca?" "My health. I came to Casablanca for the waters." "The
waters? What waters? We're in the desert." "I was misinformed."
0
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