An article manufactured by a company consists of two parts A and B. In the process of manufacture of part A 9 out of 100 are likely to be defective. Similarly, 5 out of 100 are likely to be defective in the manufacture of part B. Calculate the probability that assembled parts will not be defective.

To find the probability that the assembled article will not be defective, we first need to determine the probabilities of each part being non-defective.

Step 1: Calculate Non-Defective Probabilities

For part A, the probability of being defective is 9 out of 100, which means:

• Probability of A being defective: P(A defective) = 9/100 = 0.09
• Probability of A being non-defective: P(A non-defective) = 1 - P(A defective) = 1 - 0.09 = 0.91

For part B, the probability of being defective is 5 out of 100, so:

• Probability of B being defective: P(B defective) = 5/100 = 0.05
• Probability of B being non-defective: P(B non-defective) = 1 - P(B defective) = 1 - 0.05 = 0.95

Step 2: Calculate the Probability of Both Parts Being Non-Defective

The probability that both parts A and B are non-defective can be found by multiplying their individual probabilities:

P(A and B non-defective) = P(A non-defective) × P(B non-defective)

Substituting the values we calculated:

P(A and B non-defective) = 0.91 × 0.95

Step 3: Perform the Calculation

Now, let's do the multiplication:

P(A and B non-defective) = 0.91 × 0.95 = 0.8655

Final Result

The probability that the assembled parts will not be defective is approximately 0.8655, or 86.55%.