14. Suppose that the probability that Bob will go downtown is 45%. Now, also suppose that if Bob goes downtown, then the probability that he will stop by a coffee shop is 68%. Find the probability that Bob will go downtown and stop at a coffee shop. A. 0.306 B. 0.326 C. 0.346 D. 0.366
14. Suppose that the probability that Bob will go downtown is 45%. Now, also suppose that if Bob goes downtown, then the probability that he will stop by a coffee shop is 68%. Find the probability that Bob will go downtown and stop at a coffee shop. A. 0.306 B. 0.326 C. 0.346 D. 0.366
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Problem 14: Calculating Joint Probability**
Suppose that the probability that Bob will go downtown is 45%. Now, also suppose that if Bob goes downtown, the probability that he will stop by a coffee shop is 68%. Find the probability that Bob will go downtown and stop at a coffee shop.
**Options:**
A. 0.306
B. 0.326
C. 0.346
D. 0.366
To solve the problem, use the formula for joint probability:
\[ P(A \text{ and } B) = P(A) \times P(B|A) \]
Where:
- \( P(A) \) is the probability that Bob goes downtown.
- \( P(B|A) \) is the probability that Bob stops at a coffee shop given that he goes downtown.
Substitute the given probabilities:
\[ P(A \text{ and } B) = 0.45 \times 0.68 = 0.306 \]
Thus, the probability that Bob will go downtown and stop at a coffee shop is **0.306**. The correct answer is **A**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F989374ce-3c35-4f4d-b4d6-005e01ca096b%2F6522f789-ad36-4f90-b821-09eae74bcb38%2Fniqzixg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 14: Calculating Joint Probability**
Suppose that the probability that Bob will go downtown is 45%. Now, also suppose that if Bob goes downtown, the probability that he will stop by a coffee shop is 68%. Find the probability that Bob will go downtown and stop at a coffee shop.
**Options:**
A. 0.306
B. 0.326
C. 0.346
D. 0.366
To solve the problem, use the formula for joint probability:
\[ P(A \text{ and } B) = P(A) \times P(B|A) \]
Where:
- \( P(A) \) is the probability that Bob goes downtown.
- \( P(B|A) \) is the probability that Bob stops at a coffee shop given that he goes downtown.
Substitute the given probabilities:
\[ P(A \text{ and } B) = 0.45 \times 0.68 = 0.306 \]
Thus, the probability that Bob will go downtown and stop at a coffee shop is **0.306**. The correct answer is **A**.
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