Hey what’s the answer to this practice work question ### Understanding Conditional Probability #### Formula for Conditional ProbabilityThe conditional probability of event A given event B is calculated using the formula:\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]#### Example TableConsider 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 |#### ProblemDetermine 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:\[ P(\text{Freshman} | \text{Boy}) = \frac{\text{Number of Freshmen boys}}{\text{Total number of boys}} = \frac{3}{10} = 0.3 \]#### AnswerSo, the probability \( P(\text{Freshman} | \text{Boy}) = 0.3 \).### PracticeYou can enter your answer and verify it by clicking 'Enter'. \[ P(\text{Freshman} | \text{Boy}) = ? \]\[ \boxed{0.3} \]

Answered: Boys Giris Freshmen 3 7 Sophomores 9…

Math

Algebra

Boys Giris Freshmen 3 7 Sophomores 9 Juniors P(Freshman Boy): = Seniors 5

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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Question

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'.

\[ P(\text{Freshman} | \text{Boy}) = ? \]
\[ \boxed{0.3} \]

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