Freddie has applied to both Gainesville College and Kennessaw Sate. He thinks the probability that GC will admit him is 0.6, the probability that KSU will admit him is 0.4, and the probability that both will admit him is 0.2. Hint (Draw a Venn Diagram and “Clean it up"!!) 9. What is the probability that he gets into KSU but not Gainesville?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A. 40%

B. 60%

C. 20%

D. 80%

**Application Probability Analysis**

Freddie has applied to both Gainesville College and Kennesaw State. He thinks the probability that Gainesville College (GC) will admit him is 0.6, the probability that Kennesaw State University (KSU) will admit him is 0.4, and the probability that both will admit him is 0.2.

*Hint (Draw a Venn Diagram and “Clean it up”!!)*

**Question 9:** What is the probability that he gets into KSU but not Gainesville?

**Detailed Explanation:**

To solve this problem, we can use a Venn Diagram to visualize the probabilities:

- Let the circle representing Gainesville College (GC) be denoted as \( P(GC) = 0.6 \).
- Let the circle representing Kennesaw State University (KSU) be denoted as \( P(KSU) = 0.4 \).
- The intersection of these circles, representing the probability of being admitted to both colleges, is given as \( P(GC \cap KSU) = 0.2 \).

**Venn Diagram Analysis:**

1. **Gainesville College (GC) only:** \( P(GC) - P(GC \cap KSU) = 0.6 - 0.2 = 0.4 \)
2. **Kennesaw State University (KSU) only:** \( P(KSU) - P(GC \cap KSU) = 0.4 - 0.2 = 0.2 \)
3. **Both Colleges:** The probability of being admitted to both colleges is given as \( 0.2 \).

Thus, the probability that Freddie gets into KSU but not Gainesville is calculated by finding the probability of being admitted to KSU only, which is \( 0.2 \).
Transcribed Image Text:**Application Probability Analysis** Freddie has applied to both Gainesville College and Kennesaw State. He thinks the probability that Gainesville College (GC) will admit him is 0.6, the probability that Kennesaw State University (KSU) will admit him is 0.4, and the probability that both will admit him is 0.2. *Hint (Draw a Venn Diagram and “Clean it up”!!)* **Question 9:** What is the probability that he gets into KSU but not Gainesville? **Detailed Explanation:** To solve this problem, we can use a Venn Diagram to visualize the probabilities: - Let the circle representing Gainesville College (GC) be denoted as \( P(GC) = 0.6 \). - Let the circle representing Kennesaw State University (KSU) be denoted as \( P(KSU) = 0.4 \). - The intersection of these circles, representing the probability of being admitted to both colleges, is given as \( P(GC \cap KSU) = 0.2 \). **Venn Diagram Analysis:** 1. **Gainesville College (GC) only:** \( P(GC) - P(GC \cap KSU) = 0.6 - 0.2 = 0.4 \) 2. **Kennesaw State University (KSU) only:** \( P(KSU) - P(GC \cap KSU) = 0.4 - 0.2 = 0.2 \) 3. **Both Colleges:** The probability of being admitted to both colleges is given as \( 0.2 \). Thus, the probability that Freddie gets into KSU but not Gainesville is calculated by finding the probability of being admitted to KSU only, which is \( 0.2 \).
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