SOLUTION: A lot consists of 20 defective and 80 non-defective items from which two items are chosen without replacement. Events A & B are defined as A = the first item chosen is defecti

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Question 1183692: A lot consists of 20 defective and 80 non-defective items from which two items
are chosen without replacement. Events A & B are defined as A = the first item
chosen is defective, B = the second item chosen is defective
a. What is the probability that both items are defective?
b. What is the probability that the second item is defective?
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52779) About Me  (Show Source):
You can put this solution on YOUR website!
.
A lot consists of 20 defective and 80 non-defective items from which two items are chosen without replacement.
a. What is the probability that both items are defective?
b. What is the probability that the second item is defective?
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Notice that in your post I took off the part which is irrelevant to its contents and shadows its true meaning. 


(a)  P = %2820%2F100%29%2A%2819%2F99%29 = 19%2F%285%2A99%29 = 19%2F495 = 0.038384    (rounded).    ANSWER


Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
A lot consists of 20 defective and 80 non-defective items from which two items
are chosen without replacement. Events A & B are defined as A = the first item
chosen is defective, B = the second item chosen is defective
a. What is the probability that both items are defective?
(20/100)(19/99) = 19/495 = 0.038383838... = 3.8383...%

b. What is the probability that the second item is defective
(20/100)(19/99)+(80/100)(20/99) = 1/5 = 0.2 = 20%


What's interesting here, that Ikleyn missed, is that if we drew n items,
where n =1,2,...,100 the probability that the nth item drawn is defective is
always 1/5 or 20%. 
 
Edwin