When the occurence of one event has no effect on the probability of the occurence of another event the events are called?
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Applied Statistics and Probability for Engineers6th EditionDouglas C. Montgomery, George C. Runger 2,026 solutions "OR" or UnionsMutually Exclusive EventsTwo events are mutually exclusive if they cannot occur at the same time. Another word that means mutually exclusive is disjoint. If two events are disjoint, then the probability of them both occurring at the same time is 0. Disjoint: P(A and B) = 0If two events are mutually exclusive, then the probability of either occurring is the sum of the probabilities of each occurring. Specific Addition RuleOnly valid when the events are mutually exclusive. P(A or B) = P(A) + P(B)Example 1:Given: P(A) = 0.20, P(B) = 0.70, A and B are disjoint I like to use what's called a joint probability distribution. (Since disjoint means nothing in common, joint is what they have in common -- so the values that go on the inside portion of the table are the intersections or "and"s of each pair of events). "Marginal" is another word for totals -- it's called marginal because they appear in the margins.
The values in red are given in the problem. The grand total is always 1.00. The rest of the values are obtained by addition and subtraction. Non-Mutually Exclusive EventsIn events which aren't mutually exclusive, there is some overlap. When P(A) and P(B) are added, the probability of the intersection (and) is added twice. To compensate for that double addition, the intersection needs to be subtracted. General Addition RuleAlways valid. P(A or B) = P(A) + P(B) - P(A and B)Example 2:Given P(A) = 0.20, P(B) = 0.70, P(A and B) = 0.15
Interpreting the tableCertain things can be determined from the joint probability distribution. Mutually exclusive events will have a probability of zero. All inclusive events will have a zero opposite the intersection. All inclusive means that there is nothing outside of those two events: P(A or B) = 1.
"AND" or IntersectionsIndependent EventsTwo events are independent if the occurrence of one does not change the probability of the other occurring. An example would be rolling a 2 on a die and flipping a head on a coin. Rolling the 2 does not affect the probability of flipping the head. If events are independent, then the probability of them both occurring is the product of the probabilities of each occurring. Specific Multiplication RuleOnly valid for independent events P(A and B) = P(A) * P(B)Example 3:P(A) = 0.20, P(B) = 0.70, A and B are independent.
The 0.14 is because the probability of A and B is the probability of A times the probability of B or 0.20 * 0.70 = 0.14. Dependent EventsIf the occurrence of one event does affect the probability of the other occurring, then the events are dependent. Conditional ProbabilityThe probability of event B occurring that event A has already occurred is read "the probability of B given A" and is written: P(B|A) General Multiplication RuleAlways works. P(A and B) = P(A) * P(B|A)Example 4:P(A) = 0.20, P(B) = 0.70, P(B|A) = 0.40 A good way to think of P(B|A) is that 40% of A is B. 40% of the 20% which was in event A is 8%, thus the intersection is 0.08.
Independence RevisitedThe following four statements are equivalent
The last two are because if two events are independent, the occurrence of one doesn't change the probability of the occurrence of the other. This means that the probability of B occurring, whether A has happened or not, is simply the probability of B occurring. Continue
with conditional probabilities. Table of Contents When the occurence of one event has no effect on the probability of the occurence of another event the events are called?What are Independent Events? In statistics and probability theory, independent events are two events wherein the occurrence of one event does not affect the occurrence of another event or events. The simplest example of such events is tossing two coins.
When the occurrence of one event has no effect on the probability of the occurrence of another event are the independent B dependent C mutually exclusive equally likely?Mutually exclusive events occur when two or more things happen at the same time. Independent events occur when the occurrence of one event has no bearing on the occurrence of another. The occurrence of one event will result in the non-occurrence of the other in mutually exclusive events.
When the occurrence of some event has no effect on the probability of occurrence of some other event the two events are said to be statistically independent?If the probability of occurrence of an event A is not affected by the occurrence of another event B, then A and B are said to be independent events. P(A) = P(A│B) = 1/2 , which implies that the occurrence of event B has not affected the probability of occurrence of the event A .
When the occurrence of one has no effect on the occurrence of the other?Two events are independent IF the occurrence of one event has NO effect on the probability that the second event will occur.
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