Patrick inspects a batch of products by sampling 4 of them without replacement. If at least one of the products is defective in the sample, the whole batch is sent back. Patrick doesn't know it, but in the batch he is inspecting now, there are 100 products and 12 are defective. If he samples 4 products from this batch without replacement,what is the probability that... a) All of the products in the sample will be defective? b) None of the products in the sample are defective? c) At least one of the products is defective and the whole batch is sent back?
Patrick inspects a batch of products by sampling 4 of them without replacement. If at least one of the products is defective in the sample, the whole batch is sent back.
Patrick doesn't know it, but in the batch he is inspecting now, there are 100 products and 12 are defective. If he samples 4 products from this batch without replacement,what is the
a) All of the products in the sample will be defective?
b) None of the products in the sample are defective?
c) At least one of the products is defective and the whole batch is sent back?
For all of the above, round to four decimal places.
(answer a b c)
Sol:-
a) The probability of selecting all 4 defective products without replacement is:
(12/100) * (11/99) * (10/98) * (9/97) = 0.00000351
Therefore, the probability that all of the products in the sample will be defective is approximately 0.0000.
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