Help me with this binomial question?

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Blonde.
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A factory is considering two methods of checking the quality of production of the batches of items it produces.
Method 1: a random sample of 10 items is taken from a large batch and the batch is accepted if there are no defectives in this sample. If there are two or more defectives the batch is rejected. If there is only 1 defective then another sample of 10 is taken and the batch is accepted if there are no defectives in the second sample, otherwise the whole batch is rejected.
Method 2: a random sample of 20 items is taken from a large batch and the batch is accepted if there is at most 1 defective in this sample, otherwise the whole batch is rejected.
The factory knows that 1% of the items produced are defective and wishes to use the method of checking the quality of production for which the probability of accepting the whole batch is largest.

a) decide which method the factory should use
b) determine the expected number of items sampled in method 1

I can't do either can someone explain it to me as the context is confusing me
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mqb2766
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(Original post by Blonde.)
A factory is considering two methods of checking the quality of production of the batches of items it produces.
Method 1: a random sample of 10 items is taken from a large batch and the batch is accepted if there are no defectives in this sample. If there are two or more defectives the batch is rejected. If there is only 1 defective then another sample of 10 is taken and the batch is accepted if there are no defectives in the second sample, otherwise the whole batch is rejected.
Method 2: a random sample of 20 items is taken from a large batch and the batch is accepted if there is at most 1 defective in this sample, otherwise the whole batch is rejected.
The factory knows that 1% of the items produced are defective and wishes to use the method of checking the quality of production for which the probability of accepting the whole batch is largest.

a) decide which method the factory should use
b) determine the expected number of items sampled in method 1

I can't do either can someone explain it to me as the context is confusing me
Probably best to break it up into bits.
Method 1, what is the probability that there are no defects in the first sample, given that the 1% probability of an item being defective?
Last edited by mqb2766; 1 year ago
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