Answer:
Probability of at most one defective component = 0.89
Step-by-step explanation:
Using the binomial distribution formula: ⁿCₓ * pˣ * qⁿ⁻ˣ
where n = number of sample
x = number of defective
p = probability of defective
q = probability of good = (1 - p)
For the question, n = 8; x = 0 or 1 (none or at most one defective); p = 0.07; q = 0.93
Probability of none defective, x = 0 :
⁸C₀ * 0.07⁰ * 0.93⁸ = 0.55
Probability of 0one defective, x= 1
⁸C₁ * 0.07¹ * 0.93⁸⁻¹ = 0.34
Probability of at most one defective component = 0.559 + 0.336 = 0.895
Probability of at most one defective component = 0.89
