11.6 Probability Involving Or and Not
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1) The probability of an event not occurring is equal to 1 minus the probability of it occurring. 2) When events are mutually exclusive, the probability of event A or B occurring is the sum of their individual probabilities. 3) When events are not mutually exclusive, the probability of event A or B occurring is the sum of their individual probabilities minus the probability of them both occurring.
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The document defines key probability terms like union, intersection, mutually exclusive events, and complement. It provides examples of calculating probabilities of compound events, such as the probability of event A or B. It explains that if events are mutually exclusive, the probability of their union is the sum of their individual probabilities. The document ends with practice problems calculating probabilities of compound events using these concepts.
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Bernoulli's Theorem: If an experiment is repeated a large number of times, the experimental probability of a particular outcome approaches a fixed number as the number of repetitions increases. (p.519)
1. Restate Bernoulli's Theorem in your own words (aimed at the level of an average nine year old).
2. If you have flipped a fair coin 99 times and gotten tails 79 of those 99 times, what is the chance that the next flip of the coin will come up tails? Why?
Experiment: Roll two distinguishable regular four-sided dice. The sides of each die are labeled 1,2,3, and 4. (You do not have to physically roll the dice. You will use this experiment for the rest of the worksheet.)
3. List all elements of the sample space. (Don't use a tree diagram unless you have to.)
4. Let G be the event that at least one die has a 3. List out the elements of event G. What do you think the probability of event G (written P(G)) is?
5. Let H be the event that both dice have even numbers. List out the elements of event H. What do you think P(H) is?
6. Let I be the event that the sum of the dice is 5. List out the elements of event I. What do you think P(I) is?
7. What is P(G
U
H)? What is P(G
U
I)? What is P(H
U
I)?
Two events are mutually exclusive if they have no elements in common. In other words, their intersection is empty.
8. Look at G;H; and I.
(a) Are G and H mutually exclusive?
(b) Are G and I mutually exclusive?
(c) Are H and I mutually exclusive?
9. Make a conjecture about P(A
U
B) for any generic events A and B that are mutually exclusive.
10. What is P(A
U
B) if A and B are NOT mutually exclusive?
11. Let J be the event that at least one die has an odd number. List out the elements of J. Which of G, H, and I is mutually exclusive to J? What is the probability of the union of that event with J?
Two events are complementary if they are mutually exclusive and P(A
U
B) = 1.
12. Without the concept of probability describe in your own words what it means for two events to be complementary?
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Example: You have 4 colors of socks in your drawer: white, black, red, and gray. You reach in and pull out a sock.
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The set of all possible outcomes is called the
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Often times, a sample space can be represented with a tree diagram.
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Bernoulli's Theorem: If an experiment is repeated a large number of times, the experimental probability of a particular outcome approaches a fixed number as the number of repetitions increases. (p.519)
1. Restate Bernoulli's Theorem in your own words (aimed at the level of an average nine year old).
2. If you have flipped a fair coin 99 times and gotten tails 79 of those 99 times, what is the chance that the next flip of the coin will come up tails? Why?
Experiment: Roll two distinguishable regular four-sided dice. The sides of each die are labeled 1,2,3, and 4. (You do not have to physically roll the dice. You will use this experiment for the rest of the worksheet.)
3. List all elements of the sample space. (Don't use a tree diagram unless you have to.)
4. Let G be the event that at least one die has a 3. List out the elements of event G. What do you think the probability of event G (written P(G)) is?
5. Let H be the event that both dice have even numbers. List out the elements of event H. What do you think P(H) is?
6. Let I be the event that the sum of the dice is 5. List out the elements of event I. What do you think P(I) is?
7. What is P(G
U
H)? What is P(G
U
I)? What is P(H
U
I)?
Two events are mutually exclusive if they have no elements in common. In other words, their intersection is empty.
8. Look at G;H; and I.
(a) Are G and H mutually exclusive?
(b) Are G and I mutually exclusive?
(c) Are H and I mutually exclusive?
9. Make a conjecture about P(A
U
B) for any generic events A and B that are mutually exclusive.
10. What is P(A
U
B) if A and B are NOT mutually exclusive?
11. Let J be the event that at least one die has an odd number. List out the elements of J. Which of G, H, and I is mutually exclusive to J? What is the probability of the union of that event with J?
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U
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Example: You have 4 colors of socks in your drawer: white, black, red, and gray. You reach in and pull out a sock.
1. What are the possible outcomes of your experiment?
The set of all possible outcomes is called the
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* Probability of green ball = g/30
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-Students will be able to discuss what constitutes reliable sources on the internet. They will learn to identify key characteristics of trustworthy information, such as credibility, accuracy, and authority. By examining different types of online sources, students will develop skills to evaluate the reliability of websites and content, ensuring they can distinguish between reputable information and misinformation.
A Visual Guide to 1 Samuel | A Tale of Two Hearts
These slides walk through the story of 1 Samuel. Samuel is the last judge of Israel. The people reject God and want a king. Saul is anointed as the first king, but he is not a good king. David, the shepherd boy is anointed and Saul is envious of him. David shows honor while Saul continues to self destruct.
HYPERTENSION - SLIDE SHARE PRESENTATION.
IT WILL BE HELPFULL FOR THE NUSING STUDENTS
IT FOCUSED ON MEDICAL MANAGEMENT AND NURSING MANAGEMENT.
HIGHLIGHTS ON HEALTH EDUCATION.
220711130083 SUBHASHREE RAKSHIT Internet resources for social science
Internet resources for social science
Contiguity Of Various Message Forms - Rupam Chandra.pptx
Contiguity Of Various Message Forms - Rupam Chandra.pptx
skeleton System.pdf (skeleton system wow)
๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ
โ โุฅุถุบ ุจูู ุฅูุฏููู
โู
ู ุฃููู ุงูู
ูุงุฒู
ุงูุชู ุตู
ู
ุชูุง
ู
ูุฒู
ุฉ ุชุดุฑูุญ ุงูุฌูุงุฒ ุงูููููู (ูุธุฑู 3)
๐๐๐๐๐๐๐๐๐๐
ุชุชู
ูุฒ ูุฐูู ุงูู
ูุฒู
ุฉ ุจุนูุฏุฉ ู
ูู
ูุฒุงุช :
1- ู
ูุชุฑุฌู
ุฉ ุชุฑุฌู
ุฉ ุชููุงุณุจ ุฌู
ูุน ุงูู
ุณุชููุงุช
2- ุชุญุชูู ุนูู 78 ุฑุณู
ุชูุถูุญู ููู ููู
ุฉ ู
ูุฌูุฏุฉ ุจุงูู
ูุฒู
ุฉ (ููู ููู
ุฉ !!!!)
#ููู
_ู
ุงูู_ุฏุฑุฎ
3- ุฏูุฉ ุงููุชุงุจุฉ ูุงูุตูุฑ ุนุงููุฉ ุฌุฏุงู ุฌุฏุงู ุฌุฏุงู
4- ูููุงูู ุจุนุถ ุงูู
ุนููู
ุงุช ุชู
ุชูุถูุญูุง ุจุดูู ุชูุตููู ุฌุฏุงู (ุชูุนุชุจุฑ ูุฏู ุงูุทุงูุจ ุฃู ุงูุทุงูุจุฉ ุจุฅููุง ู
ุนููู
ุงุช ู
ูุจูู
ุฉ ูู
ุน ุฐูู ุชู
ุชูุถูุญ ูุฐูู ุงูู
ุนููู
ุงุช ุงูู
ูุจูู
ุฉ ุจุดูู ุชูุตููู ุฌุฏุงู
5- ุงูู
ูุฒู
ุฉ ุชุดุฑุญ ููุณูุง ุจ ููุณูุง ุจุณ ุชููู ุชุนุงู ุงูุฑุงูู
6- ุชุญุชูู ุงูู
ูุฒู
ุฉ ูู ุงูู ุณูุงูุฏ ุนูู ุฎุงุฑุทุฉ ุชุชุถู
ู ุฌู
ูุน ุชูุฑูุนุงุช ู
ุนููู
ุงุช ุงูุฌูุงุฒ ุงูููููู ุงูู
ุฐููุฑุฉ ูู ูุฐูู ุงูู
ูุฒู
ุฉ
ูุงุฎูุฑุงู ูุฐูู ุงูู
ูุฒู
ุฉ ุญูุงูู ุนูููู
ูุฅุชู
ูู ู
ููู
ุฅู ุชุฏุนููู ุจุงูุฎูุฑ ูุงูุตุญุฉ ูุงูุนุงููุฉ ููุท
ูู ุงูุชูููู ุฒู
ูุงุฆู ูุฒู
ููุงุชู ุ ุฒู
ูููู
ู
ุญู
ุฏ ุงูุฐูุจู ๐๐
๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ
Diversity Quiz Prelims by Quiz Club, IIT Kanpur
Prelims of Diversity Quiz, conducted by Quiz Club, IIT Kanpur in collaboration with Unmukt on 22 June 2024.
Creative Restart 2024: Mike Martin - Finding a way around โnoโ
Ideas that are good for business and good for the world that we live in, are what Iโm passionate about.
Some ideas take a year to make, some take 8 years. I want to share two projects that best illustrate this and why it is never good to stop at โnoโ.
A Free 200-Page eBook ~ Brain and Mind Exercise.pptx
(A Free eBook comprising 3 Sets of Presentation of a selection of Puzzles, Brain Teasers and Thinking Problems to exercise both the mind and the Right and Left Brain. To help keep the mind and brain fit and healthy. Good for both the young and old alike.
Answers are given for all the puzzles and problems.)
With Metta,
Bro. Oh Teik Bin ๐๐ค๐ค๐ฅฐ
How to Fix [Errno 98] address already in use
This slide will represent the cause of the error โ[Errno 98] address already in useโ and the troubleshooting steps to resolve this error in Odoo.
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
The recent surge in pro-Palestine student activism has prompted significant responses from universities, ranging from negotiations and divestment commitments to increased transparency about investments in companies supporting the war on Gaza. This activism has led to the cessation of student encampments but also highlighted the substantial sacrifices made by students, including academic disruptions and personal risks. The primary drivers of these protests are poor university administration, lack of transparency, and inadequate communication between officials and students. This study examines the profound emotional, psychological, and professional impacts on students engaged in pro-Palestine protests, focusing on Generation Z's (Gen-Z) activism dynamics. This paper explores the significant sacrifices made by these students and even the professors supporting the pro-Palestine movement, with a focus on recent global movements. Through an in-depth analysis of printed and electronic media, the study examines the impacts of these sacrifices on the academic and personal lives of those involved. The paper highlights examples from various universities, demonstrating student activism's long-term and short-term effects, including disciplinary actions, social backlash, and career implications. The researchers also explore the broader implications of student sacrifices. The findings reveal that these sacrifices are driven by a profound commitment to justice and human rights, and are influenced by the increasing availability of information, peer interactions, and personal convictions. The study also discusses the broader implications of this activism, comparing it to historical precedents and assessing its potential to influence policy and public opinion. The emotional and psychological toll on student activists is significant, but their sense of purpose and community support mitigates some of these challenges. However, the researchers call for acknowledging the broader Impact of these sacrifices on the future global movement of FreePalestine.
220711130082 Srabanti Bag Internet Resources For Natural Science
Internet resources for natural science
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NIPER JEE PYQ
NIPER JEE QUESTIONS
MOST FREQUENTLY ASK QUESTIONS
NIPER MEMORY BASED QUWSTIONS
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Information and Communication Technology in Education
Information and Communication Technology in Education
ย
220711130088 Sumi Basak Virtual University EPC 3.pptx
220711130088 Sumi Basak Virtual University EPC 3.pptx
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220711130083 SUBHASHREE RAKSHIT Internet resources for social science
220711130083 SUBHASHREE RAKSHIT Internet resources for social science
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Contiguity Of Various Message Forms - Rupam Chandra.pptx
Contiguity Of Various Message Forms - Rupam Chandra.pptx
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Creative Restart 2024: Mike Martin - Finding a way around โnoโ
Creative Restart 2024: Mike Martin - Finding a way around โnoโ
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A Free 200-Page eBook ~ Brain and Mind Exercise.pptx
A Free 200-Page eBook ~ Brain and Mind Exercise.pptx
ย
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
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220711130082 Srabanti Bag Internet Resources For Natural Science
220711130082 Srabanti Bag Internet Resources For Natural Science
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NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...
NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...
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11.6 Probability Involving Or and Not
- 1. 11.6 Probabilities Involving NOT and OR
- 2. Problem 1 Imagine throwing a die. What is the probability of getting a 2? What is the probability of not getting a 2?
- 3. Probability of an Event NOT occurring (a.k.a. P (NOT) ) The probability that an event E will not occur is equal to 1 minus the probability that it will occur P (not E) = 1 โ P (E)
- 4. Sample Problems (# 2) If you throw a die, what is the probability of not getting an even number? If you are dealt one card from a standard 52-deck card, what is the probability of not getting A king? A heart? A picture card?
- 5. Problem # 3 Assume that it is equally probable that the pointer will land on any one of the five numbered spaces. Find the probability of not getting a 2 Find the probability of not getting an odd number
- 6. ODDS Odds in favor of an event = P (E) P (not E) Odds against E = P (not E) P (E) Note: Odds in favor and odds against are reciprocals.
- 7. Sample Problems (#4) In a standard 52-deck card, Find the odds in favor of getting a king Find the odds against getting a diamond Find the odds in favor of getting a black ace Find the odds against getting a red picture card
- 8. Sample Problems (# 5) If you toss 2 coins together, the possible outcomes are {HH, HT, TH, TT} Find the odds in favor of getting two heads Find the odds against getting a head and a tail.
- 9. Odds to Probability If the odds in favor of event E are a to b, then the probability of the event is P(E) = a a + b Example: The odds in favor of winning a horse winning a race are 2 to 5. What is the probability that the horse will win?
- 10. Probabilities Involving OR Mutually exclusive events โ events that occur simultaneously If A and B are mutually exclusive events, then P(A or B) = P (A) + P(B) Example: In a standard 52-deck card, what is the probability of getting a king or a queen?
- 11. Sample Problems (# 6) If you roll a single die, what is the probability of getting: 3 or a 5 A number less than 3 or number greater than 4
- 12. Probabilities Involving OR What if the events are not mutually exclusive? OR Probabilities with events that are not mutually exclusive If A and B are not mutually exclusive, then P(A or B) = P(A) + P(B) โ P (A and B) Suppose youโre asked to pick a card from a standard 52-deck card. What is the probability of getting a king or a diamond?
- 13. Sample Problems (# 7) Assume that it is equally probable that the pointer will land on any one of the five numbered spaces. What is the probability of getting a number greater than 2 or an odd number? What is the probability of getting an odd number or a number less than or equal to 3?
- 14. Assignment Class work: pages 601-602, #s 5, 9, 15, 23, 33 HW: pages 601-603, #s 2-66 (even)