Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Hey what’s the answer to this practice work question
![### Understanding Conditional Probability
#### Formula for Conditional Probability
The conditional probability of event A given event B is calculated using the formula:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]
#### Example Table
Consider the following distribution of boys and girls across different high school grades:
| | Freshmen | Sophomores | Juniors | Seniors |
|--------|----------|------------|---------|---------|
| **Boys** | 3 | 1 | 4 | 2 |
| **Girls** | 7 | 9 | 6 | 5 |
#### Problem
Determine the probability that a randomly chosen boy is a Freshman, denoted as \( P(\text{Freshman} | \text{Boy}) \).
To solve this, we need to know two things:
1. The total number of boys.
2. The number of Freshmen boys.
Let's calculate them:
**Total number of boys:**
\[ 3 (Freshmen) + 1 (Sophomores) + 4 (Juniors) + 2 (Seniors) = 10 \]
**Number of Freshmen boys:**
\[ 3 \]
Using the conditional probability formula:
\[ P(\text{Freshman} | \text{Boy}) = \frac{\text{Number of Freshmen boys}}{\text{Total number of boys}} = \frac{3}{10} = 0.3 \]
#### Answer
So, the probability \( P(\text{Freshman} | \text{Boy}) = 0.3 \).
### Practice
You can enter your answer and verify it by clicking 'Enter'.
\[ P(\text{Freshman} | \text{Boy}) = ? \]
\[ \boxed{0.3} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66c912c6-a327-4873-9511-a364c6ae7474%2Feb44da50-6d84-456f-bc2d-30d422b0501d%2Fva5s6zm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Conditional Probability
#### Formula for Conditional Probability
The conditional probability of event A given event B is calculated using the formula:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]
#### Example Table
Consider the following distribution of boys and girls across different high school grades:
| | Freshmen | Sophomores | Juniors | Seniors |
|--------|----------|------------|---------|---------|
| **Boys** | 3 | 1 | 4 | 2 |
| **Girls** | 7 | 9 | 6 | 5 |
#### Problem
Determine the probability that a randomly chosen boy is a Freshman, denoted as \( P(\text{Freshman} | \text{Boy}) \).
To solve this, we need to know two things:
1. The total number of boys.
2. The number of Freshmen boys.
Let's calculate them:
**Total number of boys:**
\[ 3 (Freshmen) + 1 (Sophomores) + 4 (Juniors) + 2 (Seniors) = 10 \]
**Number of Freshmen boys:**
\[ 3 \]
Using the conditional probability formula:
\[ P(\text{Freshman} | \text{Boy}) = \frac{\text{Number of Freshmen boys}}{\text{Total number of boys}} = \frac{3}{10} = 0.3 \]
#### Answer
So, the probability \( P(\text{Freshman} | \text{Boy}) = 0.3 \).
### Practice
You can enter your answer and verify it by clicking 'Enter'.
\[ P(\text{Freshman} | \text{Boy}) = ? \]
\[ \boxed{0.3} \]
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