Probability – model for quantifying uncertainty in lifeExperiment – action or process leading to a well-defined set of outcomes, outcome is not predictableOutcome – possible outcomes of random experimentEx: tossing a coin, rolling pair of dice, measuring person’s blood pressure, observe sex of newborn childSample Space – set of all possible outcomes of an experiment; denoted by S; N denotes collection of all natural numbers (including zero)Tossing a coin: S = {Heads, Tails}Rolling dice: S = {(i, j): i = 1,…,6; j = 1,…,6}Observe sex of newborn child: S = {Boy, Girl}Event – subset of possible outcomes; event is said to occur is outcome of experiment is one of the members of event“An even number occurs in tossing a die”E = {2,4,6}“Two even numbers occur in tossing a pair of dice”E = {(i, j): i = 2,4,6; j = 2,4,6}Ex: consider experiment of flipping a coin three timesSample space:By enumeration: S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}By description: S = {(i, j, k): i, j, k = H or T}Event A that “exactly one tail was observed when flipping coin three times” and event B that “majority of coins show heads”A = {HHT, HTH, THH}B = {HHH, HHT, HTH, THH}Informally used:It is likely…It is expected…There will probably be…There is a 50-50 chance…DeMorgan’s lawComplement ruleAddition ruleAddition rule for disjoint eventsBusiness Stat Lecture 1 01/11/2012Probability – model for quantifying uncertainty in life-Experiment – action or process leading to a well-defined set of outcomes, outcome is not predictable-Outcome – possible outcomes of random experimentoEx: tossing a coin, rolling pair of dice, measuring person’s blood pressure, observe sex of newborn child-Sample Space – set of all possible outcomes of an experiment; denoted by S; N denotes collection of all natural numbers (including zero)oTossing a coin: S = {Heads, Tails}oRolling dice: S = {(i, j): i = 1,…,6; j = 1,…,6}oObserve sex of newborn child: S = {Boy, Girl}-Event – subset of possible outcomes; event is said to occur is outcome of experiment is one of the members of evento“An even number occurs in tossing a die”E = {2,4,6}o“Two even numbers occur in tossing a pair of dice”E = {(i, j): i = 2,4,6; j = 2,4,6}Ex: consider experiment of flipping a coin three times-Sample space:oBy enumeration: S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}oBy description: S = {(i, j, k): i, j, k = H or T}-Event A that “exactly one tail was observed when flipping coin threetimes” and event B that “majority of coins show heads”oA = {HHT, HTH, THH}oB = {HHH, HHT, HTH, THH}Informally used:-It is likely…-It is expected…-There will probably be…-There is a 50-50 chance…DeMorgan’s lawComplement ruleAddition ruleAddition rule for disjoint