In a certain process, the probability of producing a defective component is 0.07. (a) In a random sample of 8 chosen components, what is the probability that at most one component is defective

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

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