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.
www.tutorsglobe.com offers free tutorial and concepts of introduction to game theory, characteristics of game theory, limitations of game theory, properties of a game and classifications, get solved homework assignment help in game theory.
tutorsglobe.com consumer surplus assignment help-homework help by online theory of consumer behavior tutors
www.tutorsglobe.com offers Bedeaux or Points Scheme homework help, assignment help, case study, writing homework help, online tutoring assistance by accounting tutors.
tutorsglobe.com estimation of future cash flows assignment help-homework help by online capital budgeting and project planning tutors
tutorsglobe.com cell membrane assignment help-homework help by online cell biology tutors
tutorsglobe.com parasitic plants assignment help-homework help by online mode of nutrition tutors
tutorsglobe.com kingdom fungi assignment help-homework help by online five kingdom system of classification tutors
tutorsglobe.com oil plant–groundnut assignment help-homework help by online economic importance tutors
www.tutorsglobe.com offers configurational nomenclature homework help, assignment help, online tutoring assistance, organic chemistry solutions by online qualified tutor's help.
Now let us converse the range of computers that we see today. Even though they related to the fifth generation they can be split into dissimilar categories relies on the efficiency, size, memory and number of users
tutorsglobe.com immune system disorders assignment help-homework help by online immunology tutors
Theory and lecture notes of Public Goods all along with the key concepts of public goods, Free Rider Problem, Optimal Output Decision of Public Good, Externalities and Public Goods. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Public Goods.
Theory and lecture notes of all along with the key concepts of Correlation and Regression, Clearing Existing Data, Scatter Plots, Least Squares Regression Line, Regression Line on the Scatter Plot. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Linear Models and Scatter Plots.
www.tutorsglobe.com offers cost analysis assignment help - cost analysis homework help and cost analysis accounting projects help by online accounting tutors.
tutorsglobe.com hypersensitivity- delayed type hypersensitivity assignment help-homework help by online classification of hypersensitivity reactions tutors
1953644
Questions Asked
3689
Tutors
1489682
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!