Find the missing probability. P(B) = P(A|B) = , P(An B) = %3D 20 %3D
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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![**Example Problem: Finding a Missing Probability**
**Problem Statement:**
Find the missing probability.
Given:
\[ P(B) = \frac{9}{20}, \]
\[ P(A | B) = \frac{3}{5}, \]
\[ P(A \cap B) = ? \]
**Solution:**
To find the probability \( P(A \cap B) \), we will use the definition of conditional probability.
\[ P(A | B) = \frac{P(A \cap B)}{P(B)} \]
Given:
\[ P(A | B) = \frac{3}{5} \]
\[ P(B) = \frac{9}{20} \]
We need to find \( P(A \cap B) \).
Using the formula for conditional probability:
\[ \frac{3}{5} = \frac{P(A \cap B)}{\frac{9}{20}} \]
To solve for \( P(A \cap B) \), we multiply both sides by \( \frac{9}{20} \):
\[ P(A \cap B) = \frac{3}{5} \times \frac{9}{20} \]
\[ P(A \cap B) = \frac{27}{100} \]
Therefore, the missing probability \( P(A \cap B) \) is:
\[ P(A \cap B) = \frac{27}{100} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F546f6746-1efb-4603-b27a-da81564d98fa%2Fb810a815-df7a-4418-b440-87b2e81cab69%2F7k6j40c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Example Problem: Finding a Missing Probability**
**Problem Statement:**
Find the missing probability.
Given:
\[ P(B) = \frac{9}{20}, \]
\[ P(A | B) = \frac{3}{5}, \]
\[ P(A \cap B) = ? \]
**Solution:**
To find the probability \( P(A \cap B) \), we will use the definition of conditional probability.
\[ P(A | B) = \frac{P(A \cap B)}{P(B)} \]
Given:
\[ P(A | B) = \frac{3}{5} \]
\[ P(B) = \frac{9}{20} \]
We need to find \( P(A \cap B) \).
Using the formula for conditional probability:
\[ \frac{3}{5} = \frac{P(A \cap B)}{\frac{9}{20}} \]
To solve for \( P(A \cap B) \), we multiply both sides by \( \frac{9}{20} \):
\[ P(A \cap B) = \frac{3}{5} \times \frac{9}{20} \]
\[ P(A \cap B) = \frac{27}{100} \]
Therefore, the missing probability \( P(A \cap B) \) is:
\[ P(A \cap B) = \frac{27}{100} \]
Transcribed Image Text:The following fractions are displayed in the image:
1. \( \dfrac{21}{400} \)
2. \( \dfrac{1}{40} \)
3. \( \dfrac{27}{100} \)
4. \( \dfrac{1}{4} \)
These fractions can be used to practice fraction comparison, simplification, and conversion to decimal form. Understanding how to manipulate and interpret fractions is a foundational skill in mathematics.
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