Answered

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A manufacturing machine has a 10% defect rate. If 8 items are chosen at random, what is the probability that at least one will have a defect?

Sagot :

The probability at least one will have a defect is 1 - the probability no one will have a defect.

The probability no one will have a defect is:

[tex]\begin{gathered} \frac{90}{100}\cdot\frac{90}{100}\cdot\frac{90}{100}\cdot\frac{90}{100}\cdot\frac{90}{100}\cdot\frac{90}{100}\cdot\frac{90}{100}\cdot\frac{90}{100} \\ =(0.9)^8 \\ =0.4305 \end{gathered}[/tex]

So, the probability (P) that at least one will have a defect:

P = 1 - 0.4305

P = 0.5695 = 56.95%

Answer:

P = 0.5695 = 56.95%.

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