probability XD [Autosaved].pptx
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This document defines probability and key probability concepts: - Probability is the likelihood of an event occurring, measured from 0 (impossible) to 1 (certain). - A random experiment is one with multiple possible outcomes that cannot be predicted in advance. - The sample space includes all possible outcomes of an experiment. Events are subsets of the sample space. - Complementary events are those where one occurring means the other does not occur, and their probabilities sum to 1.
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Probability
The document provides an overview of key probability concepts including:
1. Random experiments, sample spaces, events, and the classification of events as simple, mutually exclusive, independent, and exhaustive.
2. The three main approaches to defining probability: classical, relative frequency, and subjective.
3. Important probability theorems like the addition rule, multiplication rule, and Bayes' theorem.
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This document provides an introduction to probability. It defines probability as a measure of how likely an event is to occur. Probability is expressed as a ratio of favorable outcomes to total possible outcomes. The key terms used in probability are defined, including event, outcome, sample space, and elementary events. The theoretical approach to probability is discussed, where probability is predicted without performing the experiment. Random experiments are described as those that may not produce the same outcome each time. Laws of probability are presented, such as a probability being between 0 and 1. Applications of probability in everyday life are mentioned, such as reliability testing of products. Two example probability problems are worked out.
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Probability is the branch of mathematics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur.[note 1][1][2] The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ('heads' and 'tails') are both equally probable; the probability of 'heads' equals the probability of 'tails'; and since no other outcomes are possible, the probability of either 'heads' or 'tails' is 1/2 (which could also be written as 0.5 or 50%).
These concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in areas of study such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
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Probability is a branch of mathematics used to quantify the likelihood of events occurring based on patterns of chance observed in experiments. It is defined as the ratio of favorable outcomes to total possible outcomes. Common probability terms include experiment, outcome, equally likely outcomes, sample space, event, and sample point. Probability calculations follow set rules and can be applied in various domains like gambling, science, and artificial intelligence.
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2. The three main approaches to defining probability: classical, relative frequency, and subjective.
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This document provides an introduction to probability. It defines probability as a measure of how likely an event is to occur. Probability is expressed as a ratio of favorable outcomes to total possible outcomes. The key terms used in probability are defined, including event, outcome, sample space, and elementary events. The theoretical approach to probability is discussed, where probability is predicted without performing the experiment. Random experiments are described as those that may not produce the same outcome each time. Laws of probability are presented, such as a probability being between 0 and 1. Applications of probability in everyday life are mentioned, such as reliability testing of products. Two example probability problems are worked out.
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Probability is the branch of mathematics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur.[note 1][1][2] The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ('heads' and 'tails') are both equally probable; the probability of 'heads' equals the probability of 'tails'; and since no other outcomes are possible, the probability of either 'heads' or 'tails' is 1/2 (which could also be written as 0.5 or 50%).
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probability XD [Autosaved].pptx
- 2. Probability means the possibility that an event will occur. OR a measure of the likelihood of an event (or measure of chance) is called probability.
- 4. 0 is the event which is not possible . Throwing a dice is unlikely chance. Tossing a coin is having an even chance. 1 in 4or 5 is having a likely chance. getting 1 is a certain chance
- 6. Random expirement A random experiment is possible when it satisfies the two conditions:- 1)It has more than one possible outcome 2)It is not possible to predict the outcome in advance
- 8. Sample space The set of all possible outcomes of a random experiment . It is denoted by s • Sample space:- • The set of all possible outcomes of a random experiment . It is denoted by s • Sample point:- • Elements of sample space are reffered as sample point • Event:- • A subset of a space is called an event
- 9. Impossible event:-the empty set is called impossible event Sure event :- the whole sample space is called sure event. Which occurs when expirement is performed.
- 10. Possible event:-Event that can occur, but that cannot be predicted. Sometimes, we use the expression probable event instead of possible event.
- 11. Simple event :- If an event E has only one sample point of a sample space is called simple or(elementary) event. Compound event :- If an event has more than one sample point it is called compound event.
- 14. If we toss three coins, we have a total of 2 × 2 × 2 = 8 possible outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT, as shown in Figure
- 15. When a single die is thrown, there are six possible outcomes: 1, 2, 3, 4, 5, 6 WHERE AS WHEN 2 DICES ARE THROWN THERE ARE 36 POSSIBLE OUTCOMES
- 16. Outcomes are the most basic possible results of observations or experiments. An event is a collection of one or more outcomes that share a property of interest.
- 17. A DECK OF CARDS CONTAIN 52 CARDS. IN THESE CARDS WE HAVE 26BLACK CARDS AND 26 RED CARDS.IN BLACK CARDS WE HAVE 13 SPADES AND 13 CLUB. AND IN RED CARDS WE HAVE 13 DIAMONDS AND 13 HEARTS.
- 24. Complementary events:- Two events are said to be complementary when one event occurs if and only if the other does not. The probabilities of two complimentary events add up to 1. For example, rolling a 5 or greater and rolling a 4 or less on a die are complementary events, because a roll is 5 or greater if and only if it is not 4 or less.
- 25. The Complement Rule:- The Complement Rule states that the sum of the probabilities of an event and its complement must equal 1. P(A)+P(A′)=1
- 26. 1.What is the probability of landing on yellow when you spin the spinner? There is 1 yellow space on the spinner. There are 4 equal spaces on the spinner. The chance on landing on yellow is 1 in 4. We can also write that in fraction form. 1 ___ 4
- 27. Fair or Unfair? You can also use probability to determine if a game is fair or unfair. The teacher gives 1 student spinner A and she gives another student spinner B. She then explains that to win a game the person who spins yellow the most will win. Is this game fair or unfair ? Answer: This game is unfair. The student with spinner A has less of a chance to spin yellow than the student with spinner B. Spinner A has a 1 in 4 chance. Spinner B has a 1 in 3 chance.