Question 1181553
Here's how to solve this problem using Bayes' Theorem:

**1. Define Events:**

*   N: The batch of chips came from supplier New.
*   O: The batch of chips came from other suppliers.
*   D: A randomly selected chip is defective.

**2. Given Probabilities:**

*   P(N) = 0.20 (20% of chips are from New)
*   P(O) = 1 - P(N) = 0.80 (80% of chips are from other suppliers)
*   P(D|N) = 1/10 = 0.10 (Probability of a defective chip given it's from New)
*   P(D|O) = 1/50 = 0.02 (Probability of a defective chip given it's from other suppliers)

**3. What We Want:**

We want to find P(N|D), the probability that the batch came from supplier New *given* that one chip is found to be defective.

**4. Bayes' Theorem:**

Bayes' Theorem states:

P(N|D) = [P(D|N) * P(N)] / P(D)

We need to find P(D), the overall probability of a defective chip.  We can use the law of total probability:

P(D) = P(D|N) * P(N) + P(D|O) * P(O)
P(D) = (0.10 * 0.20) + (0.02 * 0.80)
P(D) = 0.02 + 0.016
P(D) = 0.036

**5. Apply Bayes' Theorem:**

P(N|D) = (0.10 * 0.20) / 0.036
P(N|D) = 0.02 / 0.036
P(N|D) ≈ 0.556

**Answer:**

The probability that the batch of chips came from supplier New, given that one chip is defective, is approximately 0.556 or 55.6%.