a manufacturing machine has a 7% defect rate.\nif 9 items are chosen at random, what is the probability that…

a manufacturing machine has a 7% defect rate.\nif 9 items are chosen at random, what is the probability that at least one will have a defect? give your answer as a fraction or decimal out to at least 4 places.

a manufacturing machine has a 7% defect rate.\nif 9 items are chosen at random, what is the probability that at least one will have a defect? give your answer as a fraction or decimal out to at least 4 places.

Answer

Explanation:

Step1: Calculate the probability of no defect

The probability of an item having no defect is (p = 1 - 0.07=0.93). For (n = 9) independent items, the probability that all 9 have no defect is (P(X = 0)=0.93^{9}). Using a calculator, (0.93^{9}\approx0.5204).

Step2: Calculate the probability of at least one defect

The probability of at least one defect is (P(X\geq1)=1 - P(X = 0)). Substitute (P(X = 0)\approx0.5204) into the formula: (P(X\geq1)=1 - 0.5204 = 0.4796).

Answer:

(0.4796)