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An experiment is a process of making an observation or taking a
measurement. A random experiment is an experiment with uncertain
outcome. An event describes something happening in a random
experiment, it is a set consists of some elementary outcomes. ' Example: Tossing a coin is a random experiment. Obtaining a
head is an event. We are uncertain whether we will get a head or a tail
when we toss a coin. We want to find the probability of obtaining a head. Example: Measuring an individual’s height is a random
experiment. We are uncertain what the individual’s height is before the
measurement is finished. Height between 65 inches and 70 inches is an
event. We may want to find the probability that an individual’s height is between 65 inches and 70 inches. Interpretations of Probability There are three interpretations of probability. 1. Classical Definition. If an experiment can terminate in N equally likely and mutually
exclusive ways, and an event can happen in K of these ways, the probability of the event is KIN Example: Tossing a coin, the probability of getting a head is 1/2.
We have N=2, K=1. Example: Rolling a die, the probability of getting a 2' or 5 is 1/3.
Wehave N=6, K=2. 2. Frequency Theory. If the experiment can be repeated independently under the same
condition, the probability of an event is the relative frequency of
the occurrence of the event in an infinitely number of trials. Example: Tossing a thumb tack, what is the probability that it \i/ ’V will point up? We can find this probability by repeatedly
tossing the thumb tack millions and millions of times. The relative frequency that it points up Will tend to the true probability. Example: People are either right handed or left handed. What is
the probability that a randomly selected individual is left
handed? We can find this probability by observing millions
and millions of people. The relative frequency of left-handed
people will tend to the true probability. 3. Subjective Probability. Subjective probability depends on the individual’s degree of belief. Example: Wéather man/woman reports the probability of raining
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- Fall '17
- HUMPANTA
- Math