Chapter all: Probability
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The probability of some event, denoted p(e), is usually defined in such a way that p satisfies a number of rules. Equation 5. 1: approximately probability (cid:4666)(cid:4667)= (cid:1866)(cid:1873)(cid:1865)(cid:1854)(cid:1857)(cid:1870) (cid:1867)(cid:1858) (cid:1872)(cid:1870)(cid:1853)(cid:1864)(cid:1871) (cid:1867)(cid:1858) (cid:1857)(cid:1876)(cid:1868)(cid:1857)(cid:1870)(cid:1865)(cid:1857)(cid:1866)(cid:1872)= (cid:1866)(cid:1873)(cid:1865)(cid:1854)(cid:1857)(cid:1870) (cid:1867)(cid:1858) (cid:1875)(cid:1853)(cid:1877)(cid:1871) (cid:1857)(cid:1874)(cid:1857)(cid:1866)(cid:1872) (cid:1855)(cid:1853)(cid:1866) (cid:1867)(cid:1855)(cid:1855)(cid:1873)(cid:1870) (cid:1858)(cid:1870)(cid:1857)(cid:1869)(cid:1873)(cid:1857)(cid:1866)(cid:1855)(cid:1877) (cid:1867)(cid:1858) (cid:1866)(cid:1873)(cid:1865)(cid:1854)(cid:1857)(cid:1870) (cid:1867)(cid:1858) (cid:1868)(cid:1867)(cid:1871)(cid:1871)(cid:1854)(cid:1864)(cid:1857) (cid:1867)(cid:1873)(cid:1872)(cid:1855)(cid:1867)(cid:1865)(cid:1857)(cid:1871) N (e) or m = number of favorable outcomes. N (s) or n = number of total possible outcomes. These events must be mutually exclusive, meaning they are independently occurring events. Equation 5. 2: addition rule for disjoint events (cid:4666)(cid:1827) (cid:1515)(cid:1828)(cid:4667)=(cid:4666)(cid:1827)(cid:4667)+(cid:4666)(cid:1828)(cid:4667) (cid:4666)(cid:1827) (cid:1515)(cid:1828)(cid:4667) = probability of a or b occurring. Since some events are not mutually exclusive, this will require the use of the general addition rule (equation 5. 3. ) Equation 5. 3: general addition rule (cid:4666)(cid:1827) (cid:1515)(cid:1828)(cid:4667)= (cid:4666)(cid:1827)(cid:4667)+(cid:4666)(cid:1828)(cid:4667) (cid:4666)(cid:1827)(cid:1514)(cid:1828)(cid:4667) (cid:4666)(cid:1827)(cid:1514)(cid:1828)(cid:4667) = probability that both a and b could occur. The probability of an event a happening is p(a). Since all probabilities add up to 1, this means that the complement is equal to 1 p(a).