# testing probability with venn diagram

 A  company  produces  two  types  of  CDs,  CD-R
and CD-RW. The product CD-R constitutes 35%
of total production. About 5% of the company’s
production  is  defective,  of  which  40%  is  CD-R.
Suppose  a  CD  is  selected  at  random  from
today’s production.
a  Display these facts using a Venn diagram.
b  What is the probability that the selected CD is
defective?
c  What is the probability that the selected CD is
a CD-RW?

d  What is the probability that a CD-R is selected
given that a defective is the selected CD?
e  Are  the  events  “select  CD-R” and  “select  a
f   What  is  the  probability  that  a  CD-RW  is
selected   given   that   a   defective   is   the
selected CD?


Here's my answer for letter a.

where 2 is defective cd -r; 3 is defective cd-rw

letter b. P(defective) = 5/100

letter c. P(cdrw) = 65/100

letter d. (are we going to use concept of conditional probability), i ended up "2/5" given P(A) = cd selected and P(B) = defective. so its going to be (2/100) / (5/100)

letter e. P(AB) = P(A) P(B) . they are not equal to each other. so they are not independent

letter f. use P(A|B) where P(B) = defective CD ; P(A) = CD - RW. P(AB) = 3/100 while P(B) = 5/100. so the answer is 3/5

thanks math xchange

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There is a problem with the numbers in your diagram: you correctly show the 2% defective CD-Rs and 3% defective CD-RWs, though you should write the % signs.

But the total CD-Rs are 35% so the non-defective CD-Rs should be 33% (not 30%). Similarly you need to change the non-defective CD-RWs

You have (b) and (d) correct and can do (f) the same way as (d). Your answer to (c) is wrong but you can do it if you correct the diagram.

That leaves (e). The events “select CD-R” and “select a defective” are independent if the probability of selecting a defective CD-R is equal to the probability of selecting a CD-R times the probability of selecting a defective. So do the calculations to check this.

After diagram change:

Your answers to (a)-(d) are now correct (but show the percentage signs in the diagram).

For (e) they are indeed not independent. You should say 2/100 is not 35/100 times 5/100.

Your answer to (f) is correct but has got mixed up with (e)

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yeah i noticed there was something wrong in my venn. its now correct. how about e and f – WantIt Jan 23 '12 at 8:31
sorry about my venn diagram if its not that good looking – WantIt Jan 23 '12 at 8:32
i think theres something wrong here -> "For (e) they are indeed not independent. You should say 2/100 is not 35/100 times 5/100." .. isn't it 35/100 should be 32/100??? – WantIt Jan 23 '12 at 8:38
@user963499: You may be looking at your old diagram again. The probability that a CD is a CD-R is 35% (as it says in the question) – Henry Jan 23 '12 at 8:40
yeah my bad. tnx MR Henry – WantIt Jan 23 '12 at 8:45