Does this answer look like I calculated correctly. The question is in a certain population of women 4% have had breast CA, 20% are smokers, and 3% are smokers and have had breast CA. A woman is selected at random from the population. What is the probability that she has had breast CA or smokes or both. ### Explanation of Probability Problem Involving Breast Cancer and Smoking#### Instructions- **Problem Statement**: Do the problem #11 on page 78 in the Chapter 3 Review questions and exercises starting on page 76.#### DiagramThe diagram is a Venn diagram used to visualize the probabilities of two events, A and B:- **A** represents individuals with breast cancer.- **B** represents individuals who are smokers.The Venn diagram has two intersecting circles with the following data:- **Circle A (Breast Cancer)**: - Breast Cancer only: 4% (0.04)- **Circle B (Smokers)**: - Smokers only: 20% (0.20)- **Intersection of A and B (Both Breast Cancer and Smokers)**: - Both: 3% (0.03)#### Probability CalculationThe goal is to find the probability that a person has either breast cancer, smokes, or both.The formula used is: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]Where:- \( P(A \cup B) \) is the probability of having either event A or event B or both.- \( P(A) \) is the probability of having breast cancer: 0.04- \( P(B) \) is the probability of being a smoker: 0.20- \( P(A \cap B) \) is the probability of having both breast cancer and being a smoker: 0.03The calculation follows these steps:1. **Add probabilities of each individual event**: \[ P(A) + P(B) = 0.04 + 0.20 \]2. **Subtract the intersection of both events**: \[ P(A \cup B) = 0.04 + 0.20 - 0.03 \]This simplifies to:\[ P(BC \cup Sm) = 0.24 - 0.03 = 0.21 \]#### ConclusionThe probability that an individual has had breast cancer, smokes, or both is calculated to be 0.21 (21%).This exercise demonstrates how to use the addition rule of probability involving overlapping sets (events) to avoid double-counting the intersection.

Name: Does this answer look like I calculated correctly. The question is in
Uploaded: 2024-03-20T07:06:41.000Z
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Description: Does this answer look like I calculated correctly. The question is in a certain population of women 4% have had breast CA, 20% are smokers, and 3% are smokers and have had breast CA. A woman is selected at random from the population. What is the pr