BasicProbability

# BasicProbability - = Suggested Refrence-Book"INTRODUCTION...

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==================================================================== Suggested Refrence-Book "INTRODUCTION TO PROBABILITY AND STATISTICS" 10-th Edition by William Mendenhall, Robert Beaver and Barbara Beaver Duxbury Press An Imprint of Brooks/Cole Publishing Company ===================================================================== [001] An "EVENT" is an outcome of an experiment Experiment: Tossing a die, and observing the number that appears on the upper surface. The following events may occur: E1: observe a 1 E2: observe a 2 E3: observe a 3 E4: observe a 4 E5: observe a 5 E6: observe a 6 Event A: observe an even number Event B: observe a number greater than 3 [002] Two events are said to be "MUTUALLY EXCLUSIVE" if, when one event occurs, the other can't. Event E1 and event B are "mutually exclusive". Event E5 and event B are "NOT mutually exclusive".

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[003] An event that cannot be further decomposed is called a "SIMPLE EVENT" Event E1, or E2, or . .., E6 is called SIMPLE EVENT. Event A is "NOT" a simple event, because it can be decomposed into 3 simple events, such as E2, E4, and E6 [004] "SAMPLE SPACE" is a collection of all simple events. As a quick example, the sample space for "tossing a die" experiment is S = {E1, E2, E3, E4, E5, E6}, for which Event B = (4, 5, 6} Another example, tossing a quarter coin, and observe the possible SIMPLE EVENTS E1 = H (for Head), and E2 = T (for Tail). Thus, the sample S = {E1, E2} One more example, consider the following experiment: record a person's blood type. Observe the following possible SIMPLE EVENTS: E1 = blood type A E2 = blood type B E3 = blood type O E4 = blood type AB The sample space S = {E1, E2, E3, E4} [005] An Example: A person's blood type (including the Rh (+ or -) factor is recorded. The following possible outcomes (simple events) can be listed: E1 = O+ E2 = O- E3 = A+ E4 = A- E5 = B+
E6 = B- E7 = AB+ E8 = AB- [006] If an experiment is conducted "n" times, then the RELATIVE FREQUENCY of a particular occurence (or event), say E, is: Relative Frequency = Frequency/n where frequency = number of times that the event E occurred. If we let n = infinity, then the PROBABILITY of event E to occur is:

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BasicProbability - = Suggested Refrence-Book"INTRODUCTION...

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