8) (1 point) An event A will occur with probability 0.234. An event B will occur with prob- ability 0.427. The probability that both A and B will occur is 0.1987. Can we conclude events A and B are independent?
8) (1 point) An event A will occur with probability 0.234. An event B will occur with prob- ability 0.427. The probability that both A and B will occur is 0.1987. Can we conclude events A and B are independent?
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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I need help understanding how to determine independant or dependent as a decimal number in probability. Question 8
![### Exercise 5
Assume that the spinner cannot land on a line. Determine the following probabilities. Express your answer as a simplified fraction:
(a) The probability of the spinner landing on the color red.
\[ P(A) = \frac{3}{8} \]
(b) The probability of the spinner landing on the color green or red.
Using the formula:
\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \]
Given:
\[ P(A) = \frac{3}{8} \]
\[ P(B) = \frac{4}{8} \]
\[ P(A \text{ and } B) = 0 \]
Calculate:
\[ P(A \text{ or } B) = \frac{3}{8} + \frac{4}{8} - 0 = \frac{7}{8} \]
However, considering color distribution:
\[ P(A \text{ or } B) = \frac{4}{8} = \frac{1}{2} \]
### Exercise 6
Given:
\[ P(A) = 0.6 \]
\[ P(B) = 0.25 \]
\[ P(A \text{ or } B) = 0.55 \]
Determine \( P(A \text{ and } B) \):
Using:
\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \]
\[ 0.55 = 0.6 + 0.25 - P(A \text{ and } B) \]
Solve for \( P(A \text{ and } B) \):
\[ P(A \text{ and } B) = 0.6 + 0.25 - 0.55 = 0.3 \]
### Exercise 7
Given:
\[ P(A \text{ or } B) = 0.7 \]
\[ P(A) = 0.44 \]
\[ P(A \text{ and } B) = 0.22 \]
Determine \( P(B) \):
Using:
\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \]
\[ 0.7 = 0.44 + P(B) - 0.22 \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F158a4ea2-6357-461a-830b-c03aa61a4bf8%2Fa3e290c1-c0e6-4414-a4b9-8cc6a2c0eb56%2Fd5ohkte.jpeg&w=3840&q=75)
Transcribed Image Text:### Exercise 5
Assume that the spinner cannot land on a line. Determine the following probabilities. Express your answer as a simplified fraction:
(a) The probability of the spinner landing on the color red.
\[ P(A) = \frac{3}{8} \]
(b) The probability of the spinner landing on the color green or red.
Using the formula:
\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \]
Given:
\[ P(A) = \frac{3}{8} \]
\[ P(B) = \frac{4}{8} \]
\[ P(A \text{ and } B) = 0 \]
Calculate:
\[ P(A \text{ or } B) = \frac{3}{8} + \frac{4}{8} - 0 = \frac{7}{8} \]
However, considering color distribution:
\[ P(A \text{ or } B) = \frac{4}{8} = \frac{1}{2} \]
### Exercise 6
Given:
\[ P(A) = 0.6 \]
\[ P(B) = 0.25 \]
\[ P(A \text{ or } B) = 0.55 \]
Determine \( P(A \text{ and } B) \):
Using:
\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \]
\[ 0.55 = 0.6 + 0.25 - P(A \text{ and } B) \]
Solve for \( P(A \text{ and } B) \):
\[ P(A \text{ and } B) = 0.6 + 0.25 - 0.55 = 0.3 \]
### Exercise 7
Given:
\[ P(A \text{ or } B) = 0.7 \]
\[ P(A) = 0.44 \]
\[ P(A \text{ and } B) = 0.22 \]
Determine \( P(B) \):
Using:
\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \]
\[ 0.7 = 0.44 + P(B) - 0.22 \
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