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Probability

It is often difficult to completely match theoretical and experimental conditions. This difference can allow the theoretical and experimental measurements to differ. For example, the experimental SFA measurements consist of two deforming surfaces (sphere-on-flat geometry) having epoxy thicknesses of 16 and 25 µm. List of illustrations page x List of tables xii Preface xiii List of abbreviations xvi 1 Introduction 1 1.1 Interference modeling and performance evaluation 2 1.1.1 Mathematical modeling 2 1.1.2 Experimental modeling 3 1.1.3 Simulation modeling 3 1.2 Interference avoidance and coexistence strategies 4 1.2.1 Industry led activities 5.

Probability is a measure of the likelihood that an event will happen.

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When dealing with probability, the outcomes of a process are thepossible results. For example, when a die is rolled, the possibleoutcomes are 1, 2, 3, 4, 5, and 6. In mathematicallanguage, an event is a set of outcomes, which describe whatoutcomes correspond to the 'event' happening. For instance, 'rolling aneven number' is an event that corresponds to the set of outcomes{2, 4, 6}.The probability of an event, like rolling an even number, is thenumber of outcomes that constitute the event divided by the totalnumber of possible outcomes. We call the outcomes in an event its'favorable outcomes'.

If a die is rolled once, determine the probability of rolling a4: Rolling a 4 is an event with 1 favorable outcome (aroll of 4) and the total number of possible outcomes is 6 (a rollof 1, 2, 3, 4, 5, or 6

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). Thus, the probability of rollinga 4 is .
If a die is rolled once, determine the probability of rollingat least a 4: Rolling at least 4 is an event with 3favorable outcomes (a roll of 4, 5, or 6) and the total numberof possible outcomes is again 6. Thus, the probability of rolling atleast a 4 is = .

Here are two more examples:
If a coin is flipped twice, determine the probability that it will land heads both times:
Favorable outcomes: 1 -- HH
Possible outcomes: 4 -- HH, HT, TH, TT
Thus, the probability that the coin will land heads both times is .
If Dan grabs one sock from a drawer containing 3 white socks, 4 blue socks, and 5 yellow socks, what is the probability that he will grab a white sock?
Favorable outcomes: 3 (3 white socks)
Possible outcomes: 12 (3 white socks + 4 blue socks + 5 yellow socks)
Thus, the probability that Dan will grab a white sock is = .

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Though probabilities are calculated as fractions, they can beconverted to decimals or percents--the Fractions SparkNotein Pre-Algebra explains how to convert fractions to decimalsand the SparkNote on Percents describes how toconvert them to percents.

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Boundaries on Probability

If all outcomes are favorable for a certain event, its probability is 1. For example, the probability of rolling a 6 or lower on one die is = 1.

If none of the possible outcomes are favorable for a certainevent (a favorable outcome is impossible), the probability is 0.For example, the probability of rolling a 7 on one die is = 0.