A lot of 50 items is inspected by the following two =-stage plan.
(i) A first sample of 5 items is drawn without replacement. If all are good the lot is passed: if two or more are bad the lot is rejected.
(ii) If the first sample contains just one bad item, a second sample of 10 more items is drawn without replacement (from the remaining 45 items) and the lot is rejected if two or more of these are bad. Otherwise it is accented
Suppose there are 10 bad items in the lot.
a) What is the probability that the second sample is drawn and contains more than one bad item?
b) Write down an expression for the probability that the lot is accepted.