If you pick a cherry at random, what is the probability that it will be sweet?
What is the probability that you will get a seven? Suppose we draw one card from a standard deck. The probability of the second card being red depends on whether the first card is red or not, so these events are not independent. In case production is below the PPF boundary, the economy does not fully utilize its resources. I have read many texts and articles on different aspects of probability theory over the years and each seems to require differing levels of prerequisite knowledge to understand what is going on. We might be interested in knowing the probability of rolling a 6 and the coin landing on heads. Joint Probability: The probability of the intersection of two or more events. Let’s suppose we have two events: event A — tossing a fair coin, and event B — rolling a fair die. So P(A|B) term asks “what is the probability of the coin landing on heads given that I’ve rolled a 6 on the die?” This is where we intuitively understand that the outcome of tossing the coin doesn’t depend on the roll of the die. The probability of choosing a white tee shirt is [latex]\displaystyle\frac{{3}}{{7}}[/latex]. Thus the probability of drawing a Queen or a King is: [latex]\displaystyle{P}{\left({K}\in{g}{\quad\text{or}\quad}{Q}{u}{e}{e}{n}\right)}=\frac{{8}}{{52}}[/latex]. With the ‘and’ rule we had to multiply the individual probabilities. Let us keep in mind, therefore, that when we assess probabilities in terms of the ratio of favorable to all potential cases, we rely heavily on the assumption of equal probability for all outcomes. 0000019790 00000 n
Through educational planning, a country can indicate the needed change, reform and innovation, and to maximize the use of limited resources. The probability of a specified event is the chance or likelihood that it will occur. Notice there are 2 × (There are 52 cards in the pack, 26 are red and 26 are black. [latex]\displaystyle\frac{{195}}{{665}}\approx{0.2932}[/latex]. Scarcity means when economic resources are limited in supply compared to the wants which unlimited. Basic Concept:- If you reach in and randomly grab a pair of socks and a tee shirt, what the probability at least one is white? particular product etc. event will occur... StudyMode - Premium and Free Essays, Term Papers & Book Notes. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%. Possibility that the planned target will be met 2.2 Fundamental Concepts in Probability 2.2.4 Probability of the Union of Two Events The union of events and in space is the set of all outcomes of or (or both). A standard deck of 52 playing cards consists of four Fundamental Concepts of Probability ECE275A { Lecture Supplement { Fall 2008 Ken Kreutz-Delgado Electrical and Computer Engineering Jacobs School of Engineering [latex]\displaystyle\frac{{15}}{{665}}\approx{.0226}[/latex]. Note that the ∪ symbol is known as ‘union’ and is used in the ‘or’ scenario. [latex]\displaystyle\frac{{6}}{{10}}\times\frac{{3}}{{7}}=\frac{{18}}{{70}}=\frac{{9}}{{35}}[/latex]. Now you put those 26 cards face down and pick a card randomly. If you randomly reach in and pull out a pair of socks and a tee shirt, what is the probability both are white? Bayes’Theorem Learning Objectives • Understand the basic foundations of probability analysis • Learn the probability rules for conditional probability and joint probability Say the opportunity cost for producing two products is constant, and then I draw the PPF as a straight line. 0000024726 00000 n
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Suppose we roll a die and we want to know the probability of rolling a 5 or a 6. ...Basic Probability Notes
The sample space is the set of all possible simple events: {1,2,3,4,5,6}. Then the remaining n – m outcomes correspond to E not happening, thus, [latex]\displaystyle{P}{\left(\text{not }\ {E}\right)}=\frac{{{n}-{m}}}{{n}}=\frac{{n}}{{n}}-\frac{{m}}{{n}}={1}-\frac{{m}}{{n}}={1}-{P}{\left({E}\right)}[/latex], The complement of an event is the event “E doesn’t happen”. In demagnetized state, all the domains have magnetic moments point in arbitrarily random direction and the ferromagnetic material as a whole is neutral. >> Notice that the smallest possible probability is 0—if there are no outcomes that correspond with the event. TLFeBOOK
That is, P(HH) + P(HT) + P(TH) + P(TT) = 1 Marginal and Conditional Probabilities Suppose the faculty at a local school were polled as to their agreement/disagreement with the following statement: Coaches should be paid more... ...TLFeBOOK
The likelihood that the share prices of the portfolio will Betting / Speculation How could we have found this from the individual probabilities? Suppose we flipped a coin over and over and over again and it came up heads about half of the time; we would expect that in the future whenever we flipped the coin it would turn up heads about half of the time. If we roll a standard 6-sided die, describe the sample space and some simple events. Soong State University of New York at Buffalo, Buffalo, New York, USA
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Fundamental Concepts • There are two basic rules regarding the mathematics of probability: 1. For In the last example, the events were mutually exclusive, so P(A ∪ B) = P(A) + P(B). But if you toss a coin 1000 times, you are not likely to get exactly 500 heads. E using this formula: Recall that the sample space is {1,2,3,4,5,6}. Suggest other facets of educational development. The probability of both being white is Therefore P(A ∩ B) = 1/13 ✕ 1/2 = 1/26. There are occasions when we don’t have to subtract the intersection. Fundamentals of probability. Perhaps the first thing to understand is that there are different types of probability. Copyright 2004
Therefore we need to subtract the intersection.
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(Impossible event) [latex]\displaystyle{P}{\left({A}{c}{e}\right)}=\frac{{4}}{{52}}=\frac{{1}}{{13}}\approx{0.0769}[/latex]. These events are mutually exclusive because I can’t roll a 5 and a 6. Business Head Half the cards are red, so particular disease Suppose we flipped a coin and rolled a die, and wanted to know the probability of getting a head on the coin and a 6 on the die. So P (coin landing heads and rolling a 6) = P (A=heads, B=6) = 1/2 1/6 = 1/12. The starting point in economics is to measure what we can produce. (There are 52 cards in a pack of traditional playing cards and the 2 red ones are the hearts and diamonds). This is P(coin landing heads or rolling a 6) = P(A=heads ∪ B=6) = 1/2 + 1/6 - 1/12 = 6/12 + 2/12 - 1/12 = 7/12. In this scenario the result of the coin toss would be the same no matter what we rolled on the die. Probability Concepts 1. Above introduced the concept of a random variable and some notation on probability. Example: Assuming that we have a pack of traditional playing cards, an example of a marginal probability would be the probability that a card drawn from a pack is red: P(red) = 0.5. What is the probability the minutes reading is 15 or less? Educational Planning can be basis for evaluating/assessing performance of the educational system. Toy examples of events include rolling a die or pulling a coloured ball out of a bag. P(A|B) = 1/13 as we said above and P(B) = 1/2 (half of the cards are red). Statistically Independent and Dependent Events 4. FUNDAMENTALS OF PROBABILITY AND STATISTICS FOR ENGINEERS
Mathematically we write this as P(A ∪ B) = P(A) + P(B) - P(A ∩ B). FIVE Calculate probabilities applying the rules of addition and multiplication. Visually it is the intersection of the circles of two events on a Venn Diagram (see figure below). 0000005812 00000 n
As in the previous section, consider the situation of rolling a six-sided die and first compute the probability of rolling a six: the answer is P(six) =1/6. Ahmad Everyone’s infinite desires cannot be fulfilled due to scarce resources; therefore it is a limit to what our economy can produce. The PPF is used to evaluate the effectiveness of production processes if all resources in the economy are efficiently used. If anything, I hope my rambling has been accessible to you even if you have learned nothing new. We are often interested in knowing the probability of a random variable taking on a certain value. %PDF-1.3
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or a 6 on the die. T.T. These events are not independent because it is more likely that it will rain in Galveston on days it rains in Houston than on days it does not. Sample ... Random variables and random vectors. But how do we write this mathematically? 6 = 12 total outcomes. occur FUNDAMENTALS OF PROBABILITY AND STATISTICS FOR ENGINEERS
TLFeBOOK
The probability of a specified event is the chance or likelihood that it will occur. Spades and clubs are black while hearts and diamonds are red.
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