Practice problems for these concepts can be found at:
 Probability Solved Problems for Beginning Statistics
 Probability Supplementary Problems for Beginning Statistics
The classical definition of probability is appropriate when all outcomes of an experiment are equally likely. For an experiment consisting of n outcomes, the classical definition of probability assigns probability to each outcome or simple event. For an event E consisting of k outcomes, the probability of event E is given by formula (4.4):
 P(E) = (4.4)
EXAMPLE 4.8 The experiment of selecting one card randomly from a standard deck of cards has 52 equally likely outcomes. The event A1 = {club} has probability , since A_{1} consists of 13 outcomes. The event A_{2} = {red card} has probability , since A_{2} consists of 26 outcomes. The event A_{3} = {face card (Jack, Queen, King)} has probability , since A_{3} consists of 12 outcomes.
EXAMPLE 4.9 Table 4.1 gives information concerning 50 organ transplants in the state of Nebraska during a recent year. Each patient represented in Table 4.1 had only one transplant. If one of the 50 patient records is randomly selected, the probability that the patient had a heart transplant is = .30, since 15 of the patients had heart transplants. The probability that a randomly selected patient had to wait one year or more for the transplant is = .40, since 20 of the patients had to wait one year or more. The display in Table 4.1 is called a twoway table. It displays two different variables concerning the patients.
EXAMPLE 4.10 To find the probability of the event A that the sum of the numbers on the faces of a pair of dice equals seven when a pair of dice is rolled, consider the sample space shown in Fig. 44. The event A is the six points represented by large black squares connected by the grey line in Fig. 44. The sample space consists of the 36 points shown. The probability of the event A is 6/36 or 1/6.
The classical definition of probability is not always appropriate in computing probabilities of events. If a coin is bent, heads and tails are not equally likely outcomes. If a die has been loaded, each of the six faces do not have probability of occurrence equal to . For experiments not having equally likely outcomes, the relative frequency definition of probability is appropriate. The relative frequency definition of probability states that if an experiment is performed n times, and if event E occurs f times, then the probability of event E is given by formula (4.5).
 P(E) = (4.5)
EXAMPLE 4.11 A bent coin is tossed 50 times and a head appears on 35 of the tosses. The relative frequency definition of probability assigns the probability = .70 to the event that a head occurs when this coin is tossed. A loaded die is tossed 75 times and the face "6" appears 15 times in the 75 tosses. The relative frequency definition of probability assigns the probability = .20 to the event that the face "6" will appear when this die is tossed.

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