Homework Help is Here – Start Your Trial Now!
Math
Statistics
40. Consider the events A = {wears shorts} is more likely to happen (a) Which has the higher probability, {A or B) or (A and B)? Explain. A or B since it is a union it (b) Based on your intuition, are the events A and B disjoint? Explain. No Since there is likely to be a probability of P(Aand B) (c) Based on your intuition, are the events A and B independent? Explain. Yes Since A will not effect B + vise versa and R with P(A) = 0.7 and P(B) = 0.4. (AB)

40. Consider the events A = {wears shorts} is more likely to happen (a) Which has the higher probability, {A or B) or (A and B)? Explain. A or B since it is a union it (b) Based on your intuition, are the events A and B disjoint? Explain. No Since there is likely to be a probability of P(Aand B) (c) Based on your intuition, are the events A and B independent? Explain. Yes Since A will not effect B + vise versa and R with P(A) = 0.7 and P(B) = 0.4. (AB)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
### Educational Content: Probability and Event Analysis #### Exercise 40: Analyzing Clothing Events Consider the events: - \( A = \) wears shorts - \( B = \) wears a sweatshirt - **(a)** Which has the higher probability, \( (A \text{ or } B) \) or \( (A \text{ and } B) \)? Explain. *Explanation:* \( A \text{ or } B \) since if so a union it is more likely to happen. - **(b)** Based on your intuition, are the events \( A \) and \( B \) disjoint? Explain. *Explanation:* No, since there is likely to be a probability of \( P(A \text{ and } B) \). - **(c)** Based on your intuition, are the events \( A \) and \( B \) independent? Explain. *Explanation:* No effect of wearing \( A \) with wearing \( B \), hence not independent. #### Exercise 41: Probability Assignment Consider two disjoint (or mutually exclusive) events \( A \) and \( B \) with \( P(A) = 0.7 \) and \( P(B) = 0.4 \). Are these probabilities correctly assigned? - **Hint:** Calculate \( P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \) - Calculation: \( 0.7 + 0.4 - 0 = 1.1 \) #### Exercise 42: Coin Toss Analysis The table below represents the theoretical outcomes of tossing a coin twice: | | Second Toss Heads | Second Toss Tails | Row Totals | |--------------|-------------------|-------------------|------------| | First Toss Heads | 25 | 25 | 50 | | First Toss Tails | 25 | 25 | 50 | | Column Totals | 50 | 50 | 100 | - **(a)** Are getting heads on the first toss and heads on the second toss mutually exclusive events? *Explanation:* No, they can occur simultaneously. Probability of each is calculated by considering all possible outcomes. - **(b)** Are getting heads on the first toss and heads on the second toss independent events? *Explanation
Transcribed Image Text:### Educational Content: Probability and Event Analysis #### Exercise 40: Analyzing Clothing Events Consider the events: - \( A = \) wears shorts - \( B = \) wears a sweatshirt - **(a)** Which has the higher probability, \( (A \text{ or } B) \) or \( (A \text{ and } B) \)? Explain. *Explanation:* \( A \text{ or } B \) since if so a union it is more likely to happen. - **(b)** Based on your intuition, are the events \( A \) and \( B \) disjoint? Explain. *Explanation:* No, since there is likely to be a probability of \( P(A \text{ and } B) \). - **(c)** Based on your intuition, are the events \( A \) and \( B \) independent? Explain. *Explanation:* No effect of wearing \( A \) with wearing \( B \), hence not independent. #### Exercise 41: Probability Assignment Consider two disjoint (or mutually exclusive) events \( A \) and \( B \) with \( P(A) = 0.7 \) and \( P(B) = 0.4 \). Are these probabilities correctly assigned? - **Hint:** Calculate \( P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \) - Calculation: \( 0.7 + 0.4 - 0 = 1.1 \) #### Exercise 42: Coin Toss Analysis The table below represents the theoretical outcomes of tossing a coin twice: | | Second Toss Heads | Second Toss Tails | Row Totals | |--------------|-------------------|-------------------|------------| | First Toss Heads | 25 | 25 | 50 | | First Toss Tails | 25 | 25 | 50 | | Column Totals | 50 | 50 | 100 | - **(a)** Are getting heads on the first toss and heads on the second toss mutually exclusive events? *Explanation:* No, they can occur simultaneously. Probability of each is calculated by considering all possible outcomes. - **(b)** Are getting heads on the first toss and heads on the second toss independent events? *Explanation
Expert Solution
Step 1: Determine the given data

Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved, then please specify the question number or post only that question.

The events are given as follows:

A={wears shorts}

B={wears a sweatshirt}

The probabilities for the events, {A or B} and {A and B} is defined as follows:

P(A or B)= probability that an individual wears shorts or a sweatshirt.

P(A and B)= probability that an individual wears shorts and a sweatshirt.



trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS