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.
Semiconductor memories tutorial all along with the key concepts of Capacity of Memory, Random-Access Memory, General Memory Operation, Read Only Memory, A/D and D/A converters, Digital-to-Analogue Converter, DAC circuit, Analogue-to-Digital Converter
www.tutorsglobe.com offers Variable Name and Scope homework help, assignment help, case study, writing homework help, online tutoring assistance by computer science tutors.
let phd tutors from financial management essay writing assignment help complete your essay to secure a++ at reasonable rates.
www.tutorsglobe.com - offers cost allocation homework help, cost allocation assignment help, answering questions to cost allocation accounting problems, online tutoring by live online tutors.
tutorsglobe.com pathogenesis assignment help-homework help by online candida albicans tutors
Application of the Coumarin and Chromones Ring tutorial all along with the key concepts of Warfarin, Racemic synthesis, Asymmetric hydrogenation, Hetero-Diels-Alder cycloaddition and Sodium Cromoglycate
Calorimetry tutorial all along with the key concepts of Heat and temperature, Specific heat capacity and latent heats, Experimental methods of Calorimetry and Applications of Calorimetry
tutorsglobe.com steps for computing npv assignment help-homework help by online net present value tutors
A business is formed to improve the wealth of its owners. This might come like a surprise because there are other objectives that a business might follow that are associated to the requirements of others related with the business.
tutorsglobe.com forms of corolla assignment help-homework help by online corolla tutors
Passive Filters tutorial all along with the key concepts of Band-pass filter, Band-reject filter, Notch Filter, transfer function, Low-pass filter, High-pass filter, Amplitude response of high-pass, Phase-shift filter
return on ordinary funds of shareholders, return on capital employed, operating profit margin, gross profit margin.
tutorsglobe.com karyotyping of human chromosomes assignment help-homework help by online modern genetics tutors
www.tutorsglobe.com offers Characteristics of Requirements homework help, assignment help, case study, writing homework help, online tutoring assistance by computer science tutors.
tutorsglobe.com direct elisa assignment help-homework help by online elisa tutors
1945466
Questions Asked
3689
Tutors
1495423
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!