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Question
If 18% of the bolts produced by a machine are defective, determine the probability that out of the 4 bolts chosen at random atmost 2 will be defective
Solution
p(almost 2 will be defective) = p(x ≤ 2)
= p(x = 0) + (p(x = 1) + p(x = 2)
= 4C0(0.18)°(0.82)4-0 + 4C1(0.18)1(0.82)4-1 + 4C2 (0.18)2 (0.82)4-2
= (0.82)4 + 4 × (0.18) × (0.82)3 + `(4 xx 3)/(1 xx 2)` × (0.18)2 (0.82)2
= 0.45212176 + (0.72 × 0.551368) + (6 × 0.0324 × 0.6724)
= 0.45212176 + 0.39698496 + 013071456
= 0.97982128
= 0.9798
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