### Probability of Student Characteristics#### Table and Venn Diagram Representation**Student Distribution:**| | Boys | Not boys | Total ||---------------|------|----------|-------|| **Juniors** | 65 | 35 | 100 || **Not juniors** | 220 | 145 | 365 || **Total** | 285 | 180 | 465 |**Venn Diagram Explanation:**- The Venn Diagram visually represents the data where: - The left circle represents the boys: 220 boys who are not juniors plus 65 boys who are juniors. - The right circle represents the juniors: 65 juniors who are boys plus 35 juniors who are not boys. - The overlapping section (65) indicates the number of juniors who are boys. - The values outside the circles indicate the students who are not juniors nor boys (145).#### Probability Calculations1. **Probability that a student selected at random is a boy:** \( P(B) = \frac{285}{465} \)2. **Probability that a boy selected at random is a junior:** \( P(J | B) = \frac{65}{285} \)3. **Probability of randomly choosing a student who is a junior and a boy:** \( P(J \cap B) = \frac{65}{465} \)4. **Probability of randomly choosing a student who is a girl given that she is not a junior:** \( P(G | J^c) = \frac{145}{365} \)5. **Probability of randomly selecting a girl (not a boy):** \( P(G) = \frac{180}{465} \)These probabilities help in understanding the distribution of different categories (boys, girls, juniors, not juniors) in a given student population.

The total number of students is 465.

Answered: 1. What is the probability that a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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