The greens manufacturing company makes 60% of a particular type of camera lens, the parsons company makes 15% of them, and the ratten company makes the remaining 25%. of all the camera lenses, 5% are made by greens and are defective, 10% are made by parsons and are defective, and 6% are made by ratten and are defective.. .

lens defective not defective total .
greens 5% 55% 60% .
parsons 10% 5% 15% .
ratten 6% 19% 25% .

if a camera lens is randomly selected from the general population of all lenses, what is the probability that it was not made by the ratten company, given that it is defective?

0.22

0.36

0.49

The probability is:

                              0.71

Let A denote the event it is defective

and B denote the event that it is not made by Ratten company.

             Lens Defective     Not Defective     Total .  

Greens          5%                          55%             60% .  

Parsons        10%                         5%               15% .  

Ratten            6%                          19%              25% .

Total               21%                        79%             100%

P(A)=0.21

( Since 21/100=0.21 )

P(A∩B)= 15%

( Since,  5%+10%=15%

and 15%/100%=0.15)

Hence, we are asked to find P(B|A)

We know that:

                   The answer is:

                           0.71

what statement? is there an image?

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4