GATE 2014 EC (EC3) – Question 10
A batch of 100 bulbs is inspected by testing four randomly chosen bulbs. It is rejected if any tested bulb is defective. A batch typically contains five defective bulbs. Find the probability that the current batch is accepted.
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Correct answer: 0.80 to 0.82
Explanation
Acceptance requires all four distinct sampled bulbs to be among the95good bulbs. Without replacement the probability is(95/100)(94/99)(93/98)(92/97)=**0.811875**, equivalently C(95,4)/C(100,4). This differs slightly from the with-replacement approximation0.95⁴.