Probability Rules:
‘OR’ or Unions:
Mutually Exclusive Events:
Two events are mutually exclusive when they cannot occur at similar time. Disjoint is the other word that means mutually exclusive.
When two events are disjoint, then the probability of both occurring at similar time is 0.
Disjoint: P(A and B) = 0
Whenever two events are mutually exclusive, then the probability of either occurring is the sum or addition of probabilities of each occurring.
Specific Addition Rule:
When the events are mutually exclusive then it is valid.
P(A or B) = P(A) + P(B)
Illustration: Given: P(A) = 0.20, P(B) = 0.70, A and B are disjoint
Here we can use the term joint probability distribution. As disjoint means nothing in common, and joint is what they comprise in common -- therefore the values that go on within the portion of table are intersections or "and"s of each pair of events. "Marginal" is the other word for totals – it is termed as marginal since they appear in margins.
B B' MarginalA 0.00 0.20 0.20A' 0.70 0.10 0.80Marginal 0.70 0.30 1.00The values in italic are given in the problem. The total is always 1.00. The rest of values are obtained by addition and subtraction.
Non-Mutually Exclusive Events:
In events that are not mutually exclusive, there is some overlap. When P(A) and P(B) are added, then probability of the intersection is added two times. To compensate for that double addition, the intersection requires to be subtracted.General Addition Rule:
The general addition rule is always valid for the shown below.
P(A or B) = P(A) + P(B) - P(A and B)Interpreting the table:
There are many things that can be determined by joint probability distribution. Mutually exclusive events will contain a probability of zero. All the inclusive events will contain a zero opposite to the intersection. All inclusive signifies that there is nothing outside of such two events: P(A or B) = 1.
‘AND’ or Intersections:
Independent Events: If the occurrence of one doesn’t change the probability of the other occurring then the two events are independent.
An illustration would be rolling a 2 on a die and tossing a head on a coin. Rolling the 2 doesn’t influence the probability of flipping the head.
When events are independent, then the probability of both of them occurring the product of probabilities of each occurring.
Specific Multiplication Rule:
This rule is valid for just independent events.
P(A and B) = P(A) * P(B)
Illustration: P(A) = 0.20, P(B) = 0.70, A and B are independent.
B B' MarginalA 0.14 0.06 0.20A' 0.56 0.24 0.80Marginal 0.70 0.30 1.00The answer is 0.14 since the probability of A and B is the probability of A times the probability of B or 0.20 * 0.70 = 0.14.Dependent Events:
The events are dependent whenever the occurrence of one event does influence the probability of the other.
Conditional Probability:
Probability of event B occurring that event A has already occurred is read ‘the probability of B given A’ and is written as P(B|A)
General Multiplication Rule:
This rule always works for:
P(A and B) = P(A) * P(B|A)
Illustration: P(A) = 0.20, P(B) = 0.70, P(B|A) = 0.40
An excellent way to think of P(B|A) is that 40% of A is B. 40% of the 20% that was in event A is 8%, therefore the intersection is 0.08. B B' MarginalA 0.08 0.12 0.20A' 0.62 0.18 0.80Marginal 0.70 0.30 1.00Independence Revisited:
The given four statements are equal:
• A and B are independent events• P(A and B) = P(A) * P(B)• P(A|B) = P(A)• P(B|A) = P(B)
Latest technology based Statistics Online Tutoring Assistance
Tutors, at the www.tutorsglobe.com, take pledge to provide full satisfaction and assurance in Statistics help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Statistics, project ideas and tutorials. We provide email based Statistics help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Statistics. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Statistics Homework help and assignment help services. They use their experience, as they have solved thousands of the Statistics assignments, which may help you to solve your complex issues of Statistics. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.
tutorsglobe.com receptor organs assignment help-homework help by online human physiology tutors
Theory and lecture notes of Structure of Data manager all along with the key concepts of Data management, View component, Record component, Index component, Buffer manager. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Structure of Data manager.
tutorsglobe.com simple theory of income determination assignment help-homework help by online theory of economics tutors
tutorsglobe.com blood group testing assignment help-homework help by online blood groups tutors
tutorsglobe.com periodic properties assignment help-homework help by online periodic table and its properties tutors
tutorsglobe.com principle of acceleration assignment help-homework help by online determinant of income and employment tutors
circuit theorems tutorial all along with the key concepts of millman's theorem, superposition theorem, thevenin's theorem, norton's theorem, maximum power transfer theorem, reciprocity theorem, star-delta conversions
tutorsglobe.com pathogenesis of mycetoma assignment help-homework help by online mycetoma tutors
tutorsglobe.com demand–pull inflation assignment help-homework help by online inflation and deflation tutors
tutorsglobe.com photoautotrophic bacteria assignment help-homework help by online nutrition in bacteria tutors
Cash Flows from Operating Activities, is the net outflow or inflow from trading operations, after tax payments (or receipts) and cash paid to meet financing costs.
Postulates of Quantum Mechanics tutorial all along with the key concepts of Physical meaning of the Wave-function, Quantum Mechanical Operators, Collapse of the Wave-function and Correspondence Principle
Alternative Control Strategies-SemioChemicals tutorial all along with the key concepts of Classification of Semio-Chemicals, Pheromones, Primer pheromones, Releaser pheromones and Allelochemics
tutorsglobe.com parasites assignment help-homework help by online nutrition in fungi tutors
Friction tutorial all along with the key concepts of Laws of Friction, Coefficient of Friction, Coefficient of Friction Formula, Nature of Friction, Coefficients of static and kinetic friction, Frictional Coefficient
1931869
Questions Asked
3689
Tutors
1455904
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!