A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch is rejected if even one of the four bulbs is defective. A batch typically has five defective bulbs. The probability that the current batch is accepted is __________.

GATE 2014 · General Aptitude · Probability · medium

Answer: P(batch accepted) = C(95,4)/C(100,4) ≈ 0.81. Answer: 0.81

1. Total ways to select 4 bulbs from 100: C(100,4) = 100*99*98*97 / (4*3*2*1) = 3,921,225
2. Favorable ways: all 4 bulbs from the 95 good ones: C(95,4) = 95*94*93*92 / 24 = 3,183,545
3. Compute the acceptance probability: P = 3,183,545 / 3,921,225 = (95*94*93*92)/(100*99*98*97) = 0.8119... ≈ 0.81