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 defective” independent? Justify your answer. 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