High School

RDB Co. orders 500 lathe machines from Supplier A. To decide whether to accept the supplied machines, the manager of RDB Co. tests 12 lathe machines before the delivery date. If none of the 12 randomly selected machines is found to be defective, the manager will consider the shipment acceptable.

What is the probability that none of the selected machines are defective if 10% of the batch of lathe machines are defective?

Answer :

Final answer:

The probability that none of the selected machines are defective is approximately 28.24%.

Explanation:

To find the probability that none of the selected machines are defective, we need to calculate the probability of each machine being non-defective and multiply them together. Since 10% of the batch is defective, the probability that a machine is non-defective is 1 minus the probability that it is defective, which is 1 - 0.10 = 0.90.

The probability that all 12 machines are non-defective is therefore 0.90 multiplied by itself 12 times, which is approximately 0.2824, or 28.24%.

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