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.
Polymer Solutions tutorial all along with the key concepts of Thermodynamics of Polymer Solution, Phase Equilibrium, Polymer solubility
Theory and lecture notes of Sticky-Price Equilibrium all along with the key concepts of Equilibrium on the Income-Expenditure figure, Economy Move to Equilibrium, Inventories as the Balancing Item. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Sticky-Price Equilibrium.
tutorsglobe.com dairy assignment help-homework help by online applied biology tutors
tutorsglobe.com deadlocks assignment help-homework help by online operating system tutors
Inner-Transition Elements tutorial all along with the key concepts of Characteristics of Inner-Transition Elements, Electronic Configuration and Position in Periodic Table, Atomic Radius-Oxidation States of Inner-Transition Elements and Magnetic Properties-Transition Elements
Phylum Mollusca tutorial all along with the key concepts of Features of Phylum Mollusca, Classification of Mollusca, Class Monoplacophora, Class Polyplacophora, Class Aplacophora, Class Gastropoda, Class Bivalvia, Class Scaphopoda and Class Cephalopoda
Theory and lecture notes of Six Key Indicators of Macroeconomics all along with the key concepts of unemployment rate, Real Gross Domestic Product, inflation rate, exchange rate, interest rate. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Six Key Indicators of Macroeconomics.
Structure and Function of Membranes tutorial all along with the key concepts of Structure of Membranes, Functions of Membranes, Movement of Water through Membranes, Water Potential, Osmosis and Turgor
Theory and lecture notes of Two Phase commit protocol all along with the key concepts of two phase commit protocol, recovery management, Generals paradox. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Two Phase commit protocol.
Plant-Water Relations tutorial all along with the key concepts of Cellular water relations, Stomatal mechanism, Transpiration process and Water translocation
tutorsglobe.com definition of fiscal policy assignment help-homework help by online fiscal policy tutors
www.tutorsglobe.com offers Evolution of Programming Language homework help, assignment help, case study, writing homework help, online tutoring assistance by computer science tutors.
contingency tables tutorial all along with the key concepts of chi-square distribution, properties of chi-square, chi-square testing, chi-square testing procedure
tutorsglobe.com cost of equity share capital assignment help-homework help by online capital structure tutors
tutorsglobe.com microbiology assignment help-homework help by online zoology tutors
1954278
Questions Asked
3689
Tutors
1440836
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!