Question 10 If P(C) = 0.2, P(D) = 0.3, and P(C | D) = 0.4 find P(C and D). 1) 0.06 2) 0.08 3) 0.1 4) 0.12 5) 0.5 6) 0.9 70 8) 1
Question 10 If P(C) = 0.2, P(D) = 0.3, and P(C | D) = 0.4 find P(C and D). 1) 0.06 2) 0.08 3) 0.1 4) 0.12 5) 0.5 6) 0.9 70 8) 1
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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![### Probability Question on Compound Events
**Question 10**
Given the following probabilities:
- \( P(C) = 0.2 \)
- \( P(D) = 0.3 \)
- \( P(C \mid D) = 0.4 \),
we need to calculate \( P(C \text{ and } D) \).
Choose the correct answer from the following options:
1. \( 0.06 \)
2. \( 0.08 \)
3. \( 0.1 \)
4. \( 0.12 \)
5. \( 0.5 \)
6. \( 0.9 \)
7. \( 0 \)
8. \( 1 \)
Using the formula for conditional probability:
\[ P(C \mid D) = \frac{P(C \text{ and } D)}{P(D)} \]
we can solve for \( P(C \text{ and } D) \):
\[ P(C \text{ and } D) = P(C \mid D) \times P(D) \]
Plugging in the given values:
\[ P(C \text{ and } D) = 0.4 \times 0.3 = 0.12 \]
Thus, the correct answer is:
4. \( 0.12 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a8ca984-2571-47a4-a8f9-ecaefc8de4f3%2F4b36edc9-07d6-42a8-94bc-95c5d8192e69%2F9cpvbk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability Question on Compound Events
**Question 10**
Given the following probabilities:
- \( P(C) = 0.2 \)
- \( P(D) = 0.3 \)
- \( P(C \mid D) = 0.4 \),
we need to calculate \( P(C \text{ and } D) \).
Choose the correct answer from the following options:
1. \( 0.06 \)
2. \( 0.08 \)
3. \( 0.1 \)
4. \( 0.12 \)
5. \( 0.5 \)
6. \( 0.9 \)
7. \( 0 \)
8. \( 1 \)
Using the formula for conditional probability:
\[ P(C \mid D) = \frac{P(C \text{ and } D)}{P(D)} \]
we can solve for \( P(C \text{ and } D) \):
\[ P(C \text{ and } D) = P(C \mid D) \times P(D) \]
Plugging in the given values:
\[ P(C \text{ and } D) = 0.4 \times 0.3 = 0.12 \]
Thus, the correct answer is:
4. \( 0.12 \)
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