Question

6. In a lot of 100 items, two items are randomly selected for testing, and the lot is rejected if either of the tested items is found defective.

   (a) Find the probability that a lot with k defective items is accepted. (b) Calculate this probability numerically when k = 10, 30, 50 and 70.

Answer 1

$Probability ~that~the~lot~is~accepted=\frac{\binom{k}{0}\binom{100-k}{2}}{\binom{100}{2}}=\frac{(100-k)(99-k)}{100*99}\\ For~k=10,~Probability ~that~the~lot~is~accepted=90*89/(100*99)\\ =0.8091\\ For~k=30,~Probability ~that~the~lot~is~accepted=70*69/(100*99)\\ =0.4879\\ For~k=50,~Probability ~that~the~lot~is~accepted=50*49/(100*99)\\ =0.2475\\ For~k=70,~Probability ~that~the~lot~is~accepted=30*29/(100*99)\\ =0.0879\\$