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How are experimental probability and theoretical experiment alike?
They are both estimates of the probability of outcomes that are of interest. Experimental probabilities are derived by repeating the experiment a large number of times to arrive at these estimates whereas theoretical probabilities are estimates based on a mathematical model based on some assumptions.
How are probabilities determined?
Probabilities are calculated or estimated in a variety of methods. A non-quantitative means, used by weather forecasters, is to look at general conditions, is provide probabilies based on all indicators. In this way, the probabilities reflect their belief of certain events occurring from 0 (will not occur) to 100% (certain to occur). A second wasy probabilities are determined is to collect data, and determine the relative frequency of a particular event. Perhaps 10% of all motorists drive above the speed limit in a particular area, based on data collection, so we can state the probability of a motorist speeding in a certain area is 10%. Finally, probabilities are developed based on other known probabilites or assuming equally likely outcomes. If I have 5 outcomes, and they are equally likely, then the probability of each one occurring in 20% if these outcomes are independent and mutually exclusive. If I know the chance of coin flip coming up heads is 0.50, I can determine the probability of two coins coming up heads is 0.5 x 0.5 = 0.25.
Is this independent or dependent p (drawing a face card from a deck of cards after a jack was just drawnand replaced and the deck shuffled again?
This scenario involves independent events. The probability of drawing a face card from a deck of cards does not change based on whether a jack was drawn previously because each draw is independent of the others. The replacement of the jack and shuffling of the deck reset the probabilities for each individual draw, making them independent events.
To make generalizations about future events based on inferences from data?
Prediction... Foretelling... Extrapolation...
Frequency approach for probability?
Well, that's not much of a question. Perhaps you are asking: What is the frequency interpretation of probability? This is called the classical interpretation of probability. Given n independent and identical trials with m occurrences of of a particular outcome, then the probability of this outcome, is equal to the limit of m/n as n goes to infinity. If you are asking: How can probabilities be estimated given data, based on frequency approach? A table is constructed, with intervals, and the number of events in each interval is calculated. The number of events divided by the total number of data is the relative frequency and an estimate of probability for the particular interval.
