I have been set the following question and I'm really struggling and need some advice. I think I may have completed it, but it seems too simple, so I am just after some confirmation if it's right or not.
The question is as follows:
A particular type of electronic component for use in PCs is mass produced and subject to quality control checks since it is known that 4% of all components produced in this way are defective. The quality of a day's output is monitored as follows. A sample of 15 components is drawn from the day's output (which may be assumed to be large) and inspected for defective components. If this sample contains 0 or 1 defectives the day's output is accepted , otherwise it is rejected. If it contains more than 2 defectives the output is rejected. If the sample contains 2 defectives a second sample of 15 is taken. If this sample contains 0 defectives the output is accepted, otherwise it is rejected.
So far I have worked out the following:
P(0 defectives) = 0.542
P(1 defective) = 0.339
P(2 defectives) = 0.099
I have then worked out the probably of 2 defectives and then 0 defectives in the second sample is 0.099 x 0.542 = 0.054. However I'm not sure this is correct.
I have then worked out the probability of the accepted output to be 0.542 + 0.339 + 0.054 = 0.935
I have then been asked the following:
Suppose that it is estimated that it costs £100 to inspect a sample of 15. What is the expected cost of a day's sampling?
I have simply done 100 x 0.935 = £93.50. Cost of daily sampling = £93.50.
I appreciate any help given on this