If A and B are any two events with P(A) = .3 and P(BIA) = .5, then the joint probability of A and B is: O 0.15 O 1.5 O 0.8 O 0.6
If A and B are any two events with P(A) = .3 and P(BIA) = .5, then the joint probability of A and B is: O 0.15 O 1.5 O 0.8 O 0.6
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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![### Probability Question
#### Problem Statement:
If \( A \) and \( B \) are any two events with \( P(A) = 0.3 \) and \( P(B|A) = 0.5 \), then the joint probability of \( A \) and \( B \) is:
- \( \bigcirc \) 0.15
- \( \bigcirc \) 1.5
- \( \bigcirc \) 0.8
- \( \bigcirc \) 0.6
#### Explanation:
To solve for the joint probability \( P(A \cap B) \), we use the formula for conditional probability:
\[ P(A \cap B) = P(B|A) \times P(A) \]
Given:
\( P(A) = 0.3 \) and \( P(B|A) = 0.5 \)
\[ P(A \cap B) = 0.5 \times 0.3 = 0.15 \]
Thus, the correct answer is:
- \( \bigcirc \) 0.15](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21510790-7089-4665-af28-84e860d40e43%2F9d4495e6-7f2a-439a-b53a-bcb8435538a5%2Fp1vxkui_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability Question
#### Problem Statement:
If \( A \) and \( B \) are any two events with \( P(A) = 0.3 \) and \( P(B|A) = 0.5 \), then the joint probability of \( A \) and \( B \) is:
- \( \bigcirc \) 0.15
- \( \bigcirc \) 1.5
- \( \bigcirc \) 0.8
- \( \bigcirc \) 0.6
#### Explanation:
To solve for the joint probability \( P(A \cap B) \), we use the formula for conditional probability:
\[ P(A \cap B) = P(B|A) \times P(A) \]
Given:
\( P(A) = 0.3 \) and \( P(B|A) = 0.5 \)
\[ P(A \cap B) = 0.5 \times 0.3 = 0.15 \]
Thus, the correct answer is:
- \( \bigcirc \) 0.15
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