Independent or Dependant Probability
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The document discusses independent and dependent events. Independent events are those where the occurrence of one event does not affect the other event, such as flipping a coin or rolling a die. Dependent events are those where one event affects the other, like drawing cards from a deck without replacement. The probability of dependent events decreases as the sample space decreases with each subsequent event, while independent events have an unchanged sample space and probability.
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Conditional probability is the probability of an event occurring given that another event has occurred. It is calculated as the probability of both events occurring divided by the probability of the first event. An example is given of calculating the probability of drawing two white balls in succession from an urn without replacement. The formula for conditional probability is derived as the probability of events A and B occurring divided by the probability of A. This is demonstrated using an example of finding the percentage of friends who like chocolate that also like strawberry.
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This document discusses the concept of probability. It defines probability as a measure of how likely an event is to occur. Probabilities can be described using terms like certain, likely, unlikely, and impossible. Mathematically, probabilities are often expressed as fractions, with the numerator representing the number of possible outcomes for an event and the denominator representing the total number of possible outcomes. The document provides examples to illustrate concepts like independent and conditional probabilities, as well as complementary events and the gambler's fallacy.
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This document provides an overview of probability concepts including:
- Probability is a numerical measure of the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).
- An experiment generates outcomes that make up the sample space. Events are collections of outcomes.
- Simple events have a defined probability based on being equally likely. The probability of an event is the sum of probabilities of the simple events it contains.
- Rules like the multiplication rule for independent events and additive rule for unions allow calculating probabilities of composite events.
- Complement and conditional probabilities relate the probabilities of events. Independent events do not influence each other's probabilities.
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This document provides an overview of probability concepts including:
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- An experiment generates outcomes that make up the sample space. Events are collections of outcomes.
- Simple events have a defined probability based on being equally likely. The probability of an event is the sum of probabilities of the simple events it contains.
- Rules like the multiplication rule for independent events and additive rule for unions allow calculating probabilities of composite events.
- Complement and conditional probabilities relate the probabilities of events. Independent events do not influence each other's probabilities.
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- The addition rule and multiplication rule for calculating probabilities of compound events.
- Events can be disjoint (mutually exclusive) or not disjoint.
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Probability is used to quantify an attitude of mind towards some uncertain proposition.
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2. Events are outcomes or sets of outcomes from random experiments. The probability of an event is calculated based on the number of outcomes in the event compared to the total number of possible outcomes.
3. Conditional probability is the likelihood of one event occurring given that another event has occurred. It is calculated as the probability of both events occurring divided by the probability of the first event. Conditional probabilities are useful for problems involving dependent events.
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Name Shakeel Nouman
Religion Christian
Domicile Punjab (Lahore)
Contact # 0332-4462527. 0321-9898767
E.Mail sn_gcu@yahoo.com
sn_gcu@hotmail.com
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This document discusses probability concepts through examples of independent and dependent events. It contains examples such as drawing balls from jars, tossing coins, solving problems by multiple students, selecting family members in interviews, defective light bulbs and food items, and cards from a deck. The document also provides probability questions involving sales promotions, people leaving a lift, accidentally dropped cards during shuffling, distributing balls in boxes, and a dice game between two people.
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This document discusses basic concepts of probability, including:
- The addition rule and multiplication rule for calculating probabilities of compound events.
- Events can be disjoint (mutually exclusive) or not disjoint.
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development of the concept
In 1654, a gambler Chevalier De Metre approached the well known Mathematician Blaise Pascal for certain dice problem. Pascal became interested in these problems and discussed it further with Pierre de Fermat. Both of them solved these problems independently. Since then this concept gained limelight.
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Probability is used to quantify an attitude of mind towards some uncertain proposition.
The higher the probability of an event, the more certain we are that the event will occur.
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The document defines probability as the ratio of desired outcomes to total outcomes. It provides examples of calculating probabilities of outcomes from rolling a die or flipping a coin. It explains that probabilities of all outcomes must sum to 1. It also discusses calculating probabilities of multiple events using "and" or "or", and defines experimental probability as the ratio of outcomes to trials from an experiment.
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Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
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1. Probability is the study of randomness and uncertainty of outcomes from experiments or processes. It allows us to make statements about the likelihood of events occurring.
2. Events are outcomes or sets of outcomes from random experiments. The probability of an event is calculated based on the number of outcomes in the event compared to the total number of possible outcomes.
3. Conditional probability is the likelihood of one event occurring given that another event has occurred. It is calculated as the probability of both events occurring divided by the probability of the first event. Conditional probabilities are useful for problems involving dependent events.
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This document provides an introduction to probability. It defines probability as a numerical index of the likelihood that a certain event will occur, with a value between 0 and 1. It discusses examples of using probability terms like chance and likelihood. It also covers key probability concepts such as experiments, outcomes, events, and sample spaces. It explains different types of probability including subjective, objective/classic, and empirical probabilities. It provides examples of calculating probabilities of events using various approaches.
Geometric probability distribution
1. A geometric experiment involves independent trials with two possible outcomes (success/failure), where the probability of success (p) is constant across trials.
2. The geometric random variable (X) represents the number of trials until the first success. It has a geometric distribution where P(X=x) = p(1-p)^(x-1).
3. Examples are provided to illustrate calculating the probability of success on a given trial (x), as well as the mean and standard deviation, for geometric distributions with different probabilities of success (p).
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To find the probability of two independent events:
1. Find the probability of each individual event
2. Multiply the probabilities together
To find the probability of two dependent events:
1. Find the probability of the first event
2. Find the probability of the second event given that the first event occurred
3. Multiply the probabilities together
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This document presents information on probability and its uses. It defines probability as the chances of an event occurring from a sample space. Probability is expressed as a number from 0 to 1. The document discusses different types of probability such as mathematical, statistical, and subjective probabilities. Key terminology used in probability such as sample space, outcomes, events, and complementary events are explained. Finally, the utility of probability is discussed for solving business, economic, and social problems including risk evaluation and predicting demand.
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This section discusses five methods for counting the number of possible outcomes in various situations: the multiplication counting rule, factorial rule, permutation rule, permutations rule when some items are identical, and combination rule. It provides examples of counting the number of ways to arrange presidents to visit, rank locations, select ads for different parts of a show, and choose books to review. The examples illustrate how to apply the different counting rules to determine the total number of possible outcomes.
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The addition theorem of probability states that if two events A and B are mutually exclusive, the probability of occurrence of either A or B is the sum of the individual probabilities of A and B, or P(A or B) = P(A) + P(B). The theorem can be extended to three or more mutually exclusive events. The document provides an example calculation for finding the probability that a randomly drawn ball will have a number that is a multiple of 5 or 9. It also provides an example where two people shooting at a target are not mutually exclusive events, so the formula is modified to P(A or B) = P(A) + P(B) - P(A and B).
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Name Shakeel Nouman
Religion Christian
Domicile Punjab (Lahore)
Contact # 0332-4462527. 0321-9898767
E.Mail sn_gcu@yahoo.com
sn_gcu@hotmail.com
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This will be used as part of your Personal Professional Portfolio once graded.
Objective:
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