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A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs. The probability that the current batch is accepted is
- (95/100) × (94/99) × (93/98) × (92/97)
- (95/100) × (94/99) × (93/98) × (92/97) × (91/96)
- (95/100) × (94/99) × (93/98)
- (95/100) × (94/99) × (93/98) × (92/97) × (91/96) × (90/95)
Correct answer: (95/100) × (94/99) × (93/98) × (92/97) × (91/96)
Solution
There are 95 good bulbs out of 100. For the batch to be accepted, all tested bulbs must be non-defective, so the probability is the product of successive probabilities without replacement. The keyed option corresponds to that product form.
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