Question

box A contains 4 items of which 2 are defective and box B contains 5 items of which 2 are defective.
a) What is the probability that both items are non defective.?
b) what is the probability that one item is defective and one not?
c) if one item is defective and one is not, what is the probability that the defective item came from box B?​

Answer 1

Given : box A contains 4 items of which 2 are defective and box B contains 5 items of which 2 are defective. one item from each box is selected

To find :  probability that both items are non defective.?  probability that one item is defective and one not

Solution:

box A contains 4 items of which 2 are defective

=> probability of defective from Box A = 2/4 = 1/2

probability of non defective from Box A = 1 -  1/2 = 1/2

box B contains 5 items of which 2 are defective.

probability of defective from Box B = 2/5  

probability of non defective from Box B = 1 -  2/5 = 3/5

probability that both items are non defective

= ( 1/2)(3/5)

= 3/10

3/10 is  the probability that both items are non defective

probability that one item is defective and one not?

= Defective from A  , non defective from B  + non Defective from A , defective from B

= (1/2)(3/5) + (1/2)(2/5)

= 1/2

1/2 is the that one item is defective and one not

Probability of  defective item came from box B  = (1/2)(2/5) = 1/5

if one item is defective and one is not, what is the probability that the defective item came from box B?​   =  (1/5)/(1/2)

= 2/5   is the probability  that the  the defective item came from box B

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