Transcription for Educational Website:---2. In the general population, one woman in eight will develop breast cancer. Research has shown that 1 woman in 600 carries a mutation of the BRCA gene. Eight out of 10 women with this mutation develop breast cancer. Are the events of carrying this mutation and developing breast cancer independent or dependent? Explain your answer.---This exercise discusses the probability and relationship between genetic mutations and the development of breast cancer, prompting the reader to explore whether these events are independent or dependent. **Problem Statement:**A company uses two machines to produce medical devices. Machine A produces 60% of the products and 1% of those products are defective. Machine B produces the remaining 40% of the products and 5% are defective. Given that a defective device is found, what is the probability that it was produced by Machine A?**Explanation:**To solve this problem, we can use Bayes' Theorem. We need to find the probability that a defective product is produced by Machine A.**Let's Define the Events:**- Let \( A \) be the event that a product is produced by Machine A.- Let \( D \) be the event that a product is defective.**Given:**- \( P(A) = 0.6 \) (Probability that a product is produced by Machine A)- \( P(A') = 0.4 \) (Probability that a product is produced by Machine B)- \( P(D|A) = 0.01 \) (Probability that a product is defective given it is produced by Machine A)- \( P(D|A') = 0.05 \) (Probability that a product is defective given it is produced by Machine B)**Bayes' Theorem Formula:**\[P(A|D) = \frac{P(D|A) \cdot P(A)}{P(D)}\]**Calculate \( P(D) \):**\[P(D) = P(D|A) \cdot P(A) + P(D|A') \cdot P(A')\]\[P(D) = (0.01 \cdot 0.6) + (0.05 \cdot 0.4) = 0.006 + 0.02 = 0.026\]**Calculate \( P(A|D) \):**\[P(A|D) = \frac{0.01 \cdot 0.6}{0.026} = \frac{0.006}{0.026} \approx 0.2308\]**Conclusion:**The probability that a defective device was produced by Machine A is approximately 23.08%.

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In the general population, one woman in eight will develop breast cancer. Research has shown that 1 woman in 600 carries a mutation of the BRCA gene. Eight out of 10 women with this mutation develop breast cancer. Are the events of carrying this mutation and developing breast cancer independent or dependent? Explain your answer.

In the general population, one woman in eight will develop breast cancer. Research has shown that 1 woman in 600 carries a mutation of the BRCA gene. Eight out of 10 women with this mutation develop breast cancer. Are the events of carrying this mutation and developing breast cancer independent or dependent? Explain your answer.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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