The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of eleven syringes taken from the batch. suppose the batch contains 5% defective syringes.

The probability of zero defects in the sample 0.95^11 = 0.5688
Therefore the probability of one or more defects in the sample is given by:
P(1 or more defects) = 1 - 0.5688 = 0.4312
The probability of one defect is found from:

Therefore the probability of 2 or more defects in the sample is given by:
P(1 or more defects) - P(1 defect) = 0.4312 - 0.3293 = 0.102
The probability of rejecting the batch based on the sample result is 0.102.