SOLUTION: In a factory,three machines,A,B and C, are used to manufacture plastic bottles.they produce 20%,30% and 50% respectively of the total production.1%,2%and 6% respectively of the pla

Question 1142494: In a factory,three machines,A,B and C, are used to manufacture plastic bottles.they produce 20%,30% and 50% respectively of the total production.1%,2%and 6% respectively of the plastic bottles produced by machines A,B and C defective.
6.1 Represent the information by means of a tree diagram.clearly indicate the probability associated with each branch of the tree diagram and write down all the outcomes.
6.2 A plastic bottle is selected at random from the total production.
(a) What is the probability that it was produced by machine B and it is not defective?
(b) What is the probability that the bottle is defective?
Can I get help with this please
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

6.1 Sorry... tree diagrams don't work very well in typed text. You can do that part.

A1:  machine A  and  defective:     0.20*0.01 = 0.0020
A2:  machine A  and  not defective: 0.20*0.99 = 0.1980

B1:  machine B  and  defective:     0.30*0.02 = 0.0060
B2:  machine B  and  not defective: 0.30*0.98 = 0.2940

C1:  machine C  and  defective:     0.50*0.06 = 0.0300
C2:  machine C  and  not defective: 0.50*0.94 = 0.4700
                                           ---------
                                             1.0000

6.2

(a) B2 from the table

(b) A1+B1+C1 from the table
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