Question

A component is assembled in a four-step process. The probability of making a defect in step 1 is .10; in step 2, .20; in step 3, .08; and in step 4, .05. What is the probability that the component will be defective

Answer 1

0.371

Explanation:

Given that:

Assembly requires a 4 step process:

Probability distribution of defect :

P(step 1) = 0.1

P(step 2) = 0.2

P(step 3) = 0.08

P(step 4) = 0.05

Firstly, we find the probability that there is no defect in each of the assembly process :

Probability of no defect: = (1 - p(defect))

P(step 1) = 1 - 0.1 = 0.9

P(step 2) = 1 - 0.2 = 0.8

P(step 3) = 1 - 0.08 = 0.92

P(step 4) = 1 - 0.05 = 0.95

Hence,

P(no_defect) = 0.9 * 0.8 * 0.92 * 0.95 = 0.62928

Probability of having a defective component ;

P(defect) = P(no_defect)' = 1 - p(no-defect)

1 - 0.62928 = 0.37072

0.37072

= 0.371