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With defective-component probability p = 0.02, using the geometric formula P(X=x) = p(1-p)^(x-1), what is P(x=7), the probability the first defect turns up on the seventh component tested?
A0.0200
B0.1400
C0.8800
D0.0177
Answer & Solution
Correct answer: D. 0.0177
1. The geometric pmf is P(X=x) = p(1-p)^(x-1), with p = 0.02 and x = 7.
2. P(x=7) = (0.02)(0.98)^6.
3. (0.98)^6 ≈ 0.8858, and (0.02)(0.8858) ≈ 0.0177.
4. Option B mistakes p itself for the probability of the seventh trial, and option D reports (0.98)^6 alone without multiplying by p.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.4 Geometric Distribution_
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