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If they're disjoint events:
P(A and B) = P(A) + P(B)
Generally:
P(A and B) = P(A) + P(B) - P(A|B)
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How can you state and illustrate the addition multiplication Theorem of Probability?
Addition Theorem The addition rule is a result used to determine the probability that event A or event B occurs or both occur. ; The result is often written as follows, using set notation: : ; where: : P(A) = probability that event A occurs : P(B) = probability that event B occurs : = probability that event A or event B occurs : = probability that event A and event B both occur ; For mutually exclusive events, that is events which cannot occur together: : = 0 ; The addition rule therefore reduces to : = P(A) + P(B) ; For independent events, that is events which have no influence on each other: : ; The addition rule therefore reduces to : ; Example ; Suppose we wish to find the probability of drawing either a king or a spade in a single draw from a pack of 52 playing cards. ; We define the events A = 'draw a king' and B = 'draw a spade' ; Since there are 4 kings in the pack and 13 spades, but 1 card is both a king and a spade, we have: : = 4/52 + 13/52 - 1/52 = 16/52 ; So, the probability of drawing either a king or a spade is 16/52 (= 4/13).MultiplicationTheorem The multiplication rule is a result used to determine the probability that two events, A and B, both occur. The multiplication rule follows from the definition of conditional probability. ; The result is often written as follows, using set notation: : ; where: : P(A) = probability that event A occurs : P(B) = probability that event B occurs : = probability that event A and event B occur : P(A | B) = the conditional probability that event A occurs given that event B has occurred already : P(B | A) = the conditional probability that event B occurs given that event A has occurred already ; For independent events, that is events which have no influence on one another, the rule simplifies to: : ; That is, the probability of the joint events A and B is equal to the product of the individual probabilities for the two events.
What is the or rule in probability?
Given two events, A and B, the probability of A or B is the probability of occurrence of only A, or only B or both. In mathematical terms: Prob(A or B) = Prob(A) + Prob(B) - Prob(A and B).
What is the 'and' rule in probability?
If the probability of A is p1 and probability of B is p2 where A and B are independent events or outcomes, then the probability of both A and B occurring is p1 x p2. See related link for examples.
What is the product rule and the sum rule of probability?
Sum Rule: P(A) = \sum_{B} P(A,B) Product Rule: P(A , B) = P(A) P(B|A) or P(A, B)=P(B) P(A|B) [P(A|B) means probability of A given that B has occurred] P(A, B) = P(A) P(B) , if A and B are independent events.
What is multiplication rule in probability?
Given two events, A and B, the conditional probability rule states that P(A and B) = P(A given that B has occurred)*P(B) If A and B are independent, then the occurrence (or not) of B makes no difference to the probability of A happening. So that P(A given that B has occurred) = P(A) and therefore, you get P(A and B) = P(A)*P(B)
What is addition theorem of probability?
Consider events A and B. P(A or B)= P(A) + P(B) - P(A and B) The rule refers to the probability that A can happen, or B can happen, or both can happen together. That is what is stated in the addition rule. Often P(A and B ) is zero, if they are mutually exclusive. In this case the rule just becomes P(A or B)= P(A) + P(B).
If two events A and B are mutually exclusive what does the special rule of addition state?
If two events A and B are mutually exclusive, the special rule of addition states that the probability of one or the other event's occurring equals the sum of their probabilities. This rule is expressed in the following formula:Special Rule of Addition(5-2)Equation 5-2
How can you state and illustrate the addition multiplication Theorem of Probability?
Addition Theorem The addition rule is a result used to determine the probability that event A or event B occurs or both occur. ; The result is often written as follows, using set notation: : ; where: : P(A) = probability that event A occurs : P(B) = probability that event B occurs : = probability that event A or event B occurs : = probability that event A and event B both occur ; For mutually exclusive events, that is events which cannot occur together: : = 0 ; The addition rule therefore reduces to : = P(A) + P(B) ; For independent events, that is events which have no influence on each other: : ; The addition rule therefore reduces to : ; Example ; Suppose we wish to find the probability of drawing either a king or a spade in a single draw from a pack of 52 playing cards. ; We define the events A = 'draw a king' and B = 'draw a spade' ; Since there are 4 kings in the pack and 13 spades, but 1 card is both a king and a spade, we have: : = 4/52 + 13/52 - 1/52 = 16/52 ; So, the probability of drawing either a king or a spade is 16/52 (= 4/13).MultiplicationTheorem The multiplication rule is a result used to determine the probability that two events, A and B, both occur. The multiplication rule follows from the definition of conditional probability. ; The result is often written as follows, using set notation: : ; where: : P(A) = probability that event A occurs : P(B) = probability that event B occurs : = probability that event A and event B occur : P(A | B) = the conditional probability that event A occurs given that event B has occurred already : P(B | A) = the conditional probability that event B occurs given that event A has occurred already ; For independent events, that is events which have no influence on one another, the rule simplifies to: : ; That is, the probability of the joint events A and B is equal to the product of the individual probabilities for the two events.
What is the or rule in probability?
Given two events, A and B, the probability of A or B is the probability of occurrence of only A, or only B or both. In mathematical terms: Prob(A or B) = Prob(A) + Prob(B) - Prob(A and B).
What is the 'and' rule in probability?
If the probability of A is p1 and probability of B is p2 where A and B are independent events or outcomes, then the probability of both A and B occurring is p1 x p2. See related link for examples.
What is the product rule and the sum rule of probability?
Sum Rule: P(A) = \sum_{B} P(A,B) Product Rule: P(A , B) = P(A) P(B|A) or P(A, B)=P(B) P(A|B) [P(A|B) means probability of A given that B has occurred] P(A, B) = P(A) P(B) , if A and B are independent events.
What is multiplication rule in probability?
Given two events, A and B, the conditional probability rule states that P(A and B) = P(A given that B has occurred)*P(B) If A and B are independent, then the occurrence (or not) of B makes no difference to the probability of A happening. So that P(A given that B has occurred) = P(A) and therefore, you get P(A and B) = P(A)*P(B)
What is the Addition Theorem in probability?
A compound event is any event combining two or more simple events. The notation for addition rule is: P(A or B) = P(event A occurs or event B occurs or they both occur). When finding the probability that event A occurs or event B occurs, find the total numbers of ways A can occurs and the number of ways B can occurs, but find the total in such a way that no outcome is counted more than once. General addition rule is : P(A or B) = P(A) + P(B) - P(A and B), where P(A and B) denotes that A and B both occur at the same time as an outcome in a trial procedure. It is a special addition rule that shows that A and B cannot both occur together, so P(A and B) becomes 0: If A and B are mutually exclusive, then P(A) or P(B)= P(A or B) = P(A) + P(B)
Additive rule in probability example problems with solution?
The formal addition rule is P(A or B) = P(A) + P(B) - P(A and B). A good example from the related link, from the addition rule section is: ; Suppose we wish to find the probability of drawing either a king or a spade in a single draw from a pack of 52 playing cards. ; We define the events A = 'draw a king' and B = 'draw a spade'. ; Since there are 4 kings in the pack and 13 spades, but 1 card is both a king and a spade, we have (same formula as above in symbols): : = 4/52 + 13/52 - 1/52 = 16/52 ; So, the probability of drawing either a king or a spade is 16/52 (= 4/13).
What are the rules of probability?
Basic Rules of Probability:1) The probability of an event (E) is a number (fraction or decimal) between and including 0 and 1. (0≤P(E)≤1)2) If an event (E) cannot occur its probability is 0.3) If an event (E) is certain to occur, then the probability if E is 1. This means that there is a 100% chance that something will occur.4) The sum of probabilities of all the outcomes in the sample space is 1.Addition Rules/Formulas:When two events (A and B) are mutually exclusive, meaning that they can't occur at the same time or they have no outcomes in common, the probability that A or B will occur is:P(A or B)= P(A)+P(B)If A and B are not mutually exclusive, then:P(A or B)= P(A)+P(B)-P(A and B)Multiplication Rules/Formulas:When two events (A and B) are independent events, meaning the fact that A occurs does not affect the probability of B occurring (for example flipping a coin, rolling a die, or picking a card), the probability of both occurring is:P(A and B)= P(A)P(B)Conditional Probability-When two events are dependent (not independent), the probability of both occurring is:P(A or B)= P(A)P(B|A)Note: P(B|A) does not mean B divided by A but the probability of B after A.
If two events are independent the probability that both occur is?
That probability is the product of the probabilities of the two individual events; for example, if event A has a probability of 50% and event B has a probability of 10%, the probability that both events will happen is 50% x 10% = 5%.
What does or mean in probibility?
"or" is used in the context of sets [of events] rather than probability (and certainly not probibility!),An event described as A or B means either event A or event B or both events."or" is used in the context of sets [of events] rather than probability (and certainly not probibility!),An event described as A or B means either event A or event B or both events."or" is used in the context of sets [of events] rather than probability (and certainly not probibility!),An event described as A or B means either event A or event B or both events."or" is used in the context of sets [of events] rather than probability (and certainly not probibility!),An event described as A or B means either event A or event B or both events.
