Wire manufactured by a company is tested for strength. The test gives a correct positive result with

Jaqueline Kirby 2022-06-21 Answered
Wire manufactured by a company is tested for strength. The test gives a correct positive result with a probability of 0.85 when the wire is strong, but gives an incorrect positive result (false positive) with a probability of 0.04 when in fact the wire is not strong.
If 98% of the wires are strong, and a wire chosen at random fails the test, what is the probability it really is not strong enough?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

ejigaboo8y
Answered 2022-06-22 Author has 29 answers
Events - Strong wire P ( S ) Weak Wire P ( S ) Result = P ( T ) - true positive result
P ( S ) = 0.98 P ( S ) = 0.02 P ( T | S ) = 0.85 P ( T | S ) = 0.04
P ( S | T ) = ( P ( T | S ) × P ( S ) ) / [ ( P ( T | S ) × P ( S ) ) + ( P ( T | S ) × P ( S ) ) ]
P ( S | T ) = 0.85 × 0.98 / ( 0.85 × 0.98 + 0.04 × 0.02 ) = 0.8673 / 0.8681 = 0.9991 = 99.91
99.91 % times wires are strong when tested positive
For wires tested strong and result is weak = 1 P ( S | T ) = 1 0.99 = 0.01 = 1 % So, a wire chosen from suite of strong tested wire and comes out to be weak is 1 %
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-07-11
Simplification step by step (exponential and logarithm) - regarding BLOOM FILTER - FALSE POSITIVE probability
( 1 1 m ) k n e k n / m
I don't get how to reach e k n / m from ( 1 1 m ) k n
I have reviewed logarithm and exponent rules but I always get stuck, here is what I have tried; Starting from ( 1 1 m ) k n , I can write:
- e ( l n ( 1 1 m ) k n )
- e ( k n × l n ( 1 1 m ) )
Or the other way around:
l n ( e ( 1 1 m ) k n )
l n ( e ( 1 1 m ) × k n )
l n ( e ( 1 1 m ) ) + l n ( k n )
( 1 1 m ) + l n ( k n )
After few steps I fall in an unsolvable loop hole playing with l n and e trying to reach e k n / m .
asked 2022-08-09
One in two hundred people in a population have a particular disease. A diagnosis test gives a false positive 3% of the time, and a false negative 2% of the time. Ross takes the test and the report comes positive. Find the probability that Ross has the disease.
asked 2022-06-15
A disease effects 1/1000 newborns and shortly after birth a baby is screened for this disease using a cheap test that has a 2% false positive rate (the test has no false negatives). If the baby tests positive, what is the chance it has the disease?
I've got P ( disease | positive ) = P ( d p ) P ( p ) = ( 1 / 1000 ) ( 1 / 1000 + 2 / 100 999 / 1000 ) = 1 ( 20 + 49 / 50 )
Is this right?
asked 2022-05-07
How the false positive value affects accuracy?
T P   ( t r u e   p o s i t i v e )   =   2739
T N   ( t r u e   n e g a t i v e )   =   103217
F P   ( f a l s e   p o s i t i v e )   =   43423
F N   ( f a l s e   n e g a t i v e )   =   5022
a c c u r a c y = T P + T N T P + T N + F P + F N
In this case the accuracy is 0.68. Can I say that I have low accuracy because the value false positive is high? There is any relathion between false positive and the parameters true positive or true negative?
asked 2022-07-20
True and False?
If the product A × B of two sets A and B is the empty set , then both A and B have to be empty set.
asked 2022-07-17
True and False?
If ( A B A C ) then B C
asked 2022-09-18
For any positive real number r ,   r n converges.
False: Take any positive r, then as n r diverges.
If x n y n converges, then x n and y n both converge.
False: Suppose x n or y n dont converge. Then take x n = n 2 and y n = 1 n . Then x n y n = n, which diverges. Thus it does not converge.
True or False?

New questions

I recently have this question:
I have a bag of toys. 10% of the toys are balls. 10% of the toys are blue.
If I draw one toy at random, what're the odds I'll draw a blue ball?
One person provided an answer immediately and others suggested that more details were required before an answer could even be considered. But, there was a reason I asked this question the way that I did.
I was thinking about probabilities and I was coming up with a way to ask a more complicated question on math.stackexchange.com. I needed a basic example so I came up with the toys problem I posted here.
I wanted to run it by a friend of mine and I started by asking the above question the same way. When I thought of the problem, it seemed very clear to me that the question was "what is P ( b l u e b a l l )." I thought the calculation was generally accepted to be
P ( b l u e b a l l ) = P ( b l u e ) P ( b a l l )
When I asked my friend, he said, "it's impossible to know without more information." I was baffled because I thought this is what one would call "a priori probability."
I remember taking statistics tests in high school with questions like "if you roll two dice, what're the odds of rolling a 7," "what is the probability of flipping a coin 3 times and getting three heads," or "if you discard one card from the top of the deck, what is the probability that the next card is an ace?"
Then, I met math.stackexchange.com and found that people tend to talk about "fair dice," "fair coins," and "standard decks." I always thought that was pedantic so I tested my theory with the question above and it appears you really need to specify that "the toys are randomly painted blue."
It's clear now that I don't know how to ask a question about probability.
Why do you need to specify that a coin is fair?
Why would a problem like this be "unsolvable?"
If this isn't an example of a priori probability, can you give one or explain why?
Why doesn't the Principle of Indifference allow you to assume that the toys were randomly painted blue?
Why is it that on math tests, you don't have to specify that the coin is fair or ideal but in real life you do?
Why doesn't anybody at the craps table ask, "are these dice fair?"
If this were a casino game that paid out 100 to 1, would you play?
This comment has continued being relevant so I'll put it in the post:
Here's a probability question I found online on a math education site: "A city survey found that 47% of teenagers have a part time job. The same survey found that 78% plan to attend college. If a teenager is chosen at random, what is the probability that the teenager has a part time job and plans to attend college?" If that was on your test, would you answer "none of the above" because you know the coincident rate between part time job holders and kids with college aspirations is probably not negligible or would you answer, "about 37%?"