Probability

There is one 10 of spades in a standard deck of 52 cards.

13 cards in a 52 card deck are hearts.

In a normal 52 card deck, there would be four 10 cards (10 hearts, 10 spades, 10 clubs and 10 diamonds).

One method is direct observation. Simply watch that part of the school every day at 10am, and record whether or not the person is there. Then you can determine the probability from your data set.

A more difficult method and one that is fraught with error is trying to estimate it by making a series of guesses. For example, in order for the student to be at that location, they would have to be inside the school, so, if the school is locked on a Sunday, then this probability is nearly zero. But not completely zero. What if the student broke into the school? So you can see that its very difficult to predict accurately. Many consultants are paid to do risk analysis to estimate the chances of things occurring, and their estimates usually vary so widely that its dubious if this can even be done.

The formula for Z-Score is: (x-mu)/sigma. We know from the information given that Z=0.5, mu=300 & sigma=100. Solve for x and plug in the values. X=Z*sigma+mu; x=0.5*100+300 or x=350. So, $350 is amount spent on books.

The probability of rolling an 8 is Zero.

Total number of outcomes are 6*6 or 36. There is 1 way to get a 2; which is 1,1. So, the probability is 1/36.

Overall, the probability is very close to 0.

No. The mean deviation is 0. Always.

There is insufficient information in the question to properly answer it. You need to specify, along with the 110 C's in the last three years, how many non-C's were also given out. Please restate the question.

Depends With jokers= 13/54 Without jokers= 1/4

About, but the first twin would be a few seconds older then the second

It is (4/52)*(3/51)*(2/50)*(1/49) = 1/270,725 = 0.0000037 approx.

97.61%

Exactly "what it says on the tin"! The distribution is nearly, but not quite, the standard normal, or Gaussiam distribution.

20

Rolling it once there is a 1 out of 6 chance - because there is 6 numbers on a dice and one of them is three. so rolling it twice would be a 2 out of 12 chance / 0.16 / 16% chance

11% chance that you will roll an 8 in any dice rolls

Theory Formulation http://wiki.answers.com/Q/In_what_way_is_theory_formulated 1. Theory formulation begins with fundamental presuppositions (unconscious) or assumptions (conscious). According to Collingwood (1940), fundamental assumptions are not completely provable and always have opposites. The fundamental scientific assumptions and their opposites were described by Borchardt (2004, 2007). Fundamental assumptions normally are taken for granted unless the theories they support run into serious difficulty. 2. All theories are derived from our experience with the external world. Because the external world is so vast, secondary theories tend to cover only small portions of it. Nevertheless, like the fundamental assumptions, theories ultimately are derived through observation. 3. Theory and observation is iterative. That is, they depend on each other. Animals formulate theories all the time. Herbivores observe predators eating lunch, eventually getting the idea or "theory" that the approach of a predator requires some evasive maneuver to avoid the same fate. Simple theories depend on simple observations; complex theories depend on complex observations. Complex theories are modifications of previous theories. That is why scientists must publish to advance their specialties. 4. A new theory or idea is the combination of at least two other ideas or observations. Thus, a theory, like an idea, cannot pop up out of nowhere. It always derives from other things. The incorporation of experimentation accelerated the evolution of theory formulation. With experiments, scientists were able to manipulate portions of the external world, making observations that previously were impossible. 5. Theory is instrumentally driven. The development of each new instrument multiplies the potential for observation and, correspondingly, for theory. In other words, if you want a sure topic for a thesis, get the latest instrument. 6. Theory is experientially driven. This is why students need teachers and why teachers are more likely than students to come up with the next theory. It is why half of all Nobelists studied under a Nobelist. It is why the Ph.D. program is so intensive. One needs to know what previous workers have done in the field before one can produce some new combination worthy of announcing to the world. 7. Theory partly determines what can be observed. Because the universe contains infinite detail, we must pick and choose between what is important and what is not. Thus, if we are looking south, we can know much about the south, but little, if anything, about the north. Every theory is therefore subject to errors of commission and errors of omission. The way we check for those errors is through further observation and experiment. One caution: this caveat does not mean that an unobserved portion of the universe does not exist! 8. Theories that fail a test seldom are discarded entirely. This follows from the above. The long evolution of a formerly successful theory assures that it has roots embedded in the literature and in the minds of its followers. Theories "fail" tests all the time simply because the observations and experiments were faulty. A theory can yield satisfactory explanations and predictions even though it may be incorrect. For example, we can use pre-Copernican theory to predict that the sun will rise in the morning. The sun will rise whether we think the sun goes around the earth or whether we think the earth is rotating as it goes around the sun. That particular test, by itself, cannot disprove the pre-Copernican theory. 9. As we expand our observations, theories tend to break down. Space travel would have been impossible without discarding the pre-Copernican theory. This is why science is progressive instead of cyclic (Kuhn (1970) and the post-modernists not withstanding). Because the universe is infinite, both microscopically and macroscopically (my assumption), no theory can be complete. No theory is perfect and no theory can explain and predict anything in infinite detail and with perfect precision. On the other hand, few theories are not of some use to somebody. 10. Finally, theory formulation is relatively simple. To come up with a new idea, combine two or more old ideas. As Prof. M.L. Jackson once told me: "I simply read the literature and let my brain do the connections when I am sleeping." Among scientists, much theorizing can be considered "seat of the pants" or "restaurant napkin activity." Mostly, we collect a large group of disparate observations that we think may be at least vaguely related and try to make some kind of sense of them. We do it because we are curious about what the next observation will be. If the prediction is at all successful, we may have the beginnings of a successful theory. Happy theorizing! Borchardt, G., 2004, The ten assumptions of science: Toward a new scientific worldview: Lincoln, NE, iUniverse, 125 p. Borchardt, G., 2007, The Scientific Worldview: Beyond Newton and Einstein: Lincoln, NE, iUniverse, 411 p. Collingwood, R.G., 1940, An essay on metaphysics: Oxford, Clarendon Press, 354 p. Kuhn, T.S., 1970, The structure of scientific revolutions (2 ed.): Chicago, University of Chicago Press, 210 p.

Assuming you are referring to US states, North / South could be Alaska and Florida. East / West could be California and Massachusetts.

ummm, probability?

100%

With considerable difficulty since there are a lot more than 3 possible outcomes.

From a standard deck of 52 cards, 1/52.

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