Box A contains 10 items of which 4 are defective and box B c

Box A contains 10 items of which 4 are defective, and box B contains 6 items of which 2 are defective. An kern is drawn randomly and independently from each box. a. What is the probability p that both items are nondefective? b. What is the probability p that one item is defective and one not? c. If one item is defective and one is not, what is the probability p that the defective item came from box A?

Solution

a) To gert both defective-----> we need to pick defective item from Box A and Box B

no of ways of selecting defective item from Box A = 4;

Total no of ways of selecting an item in Box A = 10

no of ways of selecting defective item from Box B = 2;

Total no of ways of selecting an item in Box B = 6

P(both are defective) = (4/10)*(2/6) = 0.1333

b) for one item to be defective and other not---> select defective ffrom Box A , non defective from Box B

or

select non defective from Box A , defective from Box B

no of ways of selecting defective item from Box A = 4;

Total no of ways of selecting an item in Box A = 10

no of ways of selecting non defective item from Box B = 4;

Total no of ways of selecting an item in Box B = 6;

no of ways of selecting non defective item from Box A = 6;

Total no of ways of selecting an item in Box A = 10

no of ways of selecting defective item from Box B = 2;

Total no of ways of selecting an item in Box B = 6;

thereofre Probability = (4/10)*(4/6) + (6/10)*(2/6) = 0.4666

c) defective item from Box 1 = from the above answer

= ((4/10)*(4/6)) /((4/10)*(4/6) + (6/10)*(2/6) ) = 0.5714