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Is there just one way of computing the probability of dependent events?
No, there isn't just one way of computing the probability of dependent events. One common method is to use the formula ( P(A \cap B) = P(A) \times P(B|A) ), where ( P(B|A) ) is the conditional probability of event B given that event A has occurred. Another approach involves constructing a probability tree or using joint probability tables, especially when dealing with multiple dependent events. The choice of method often depends on the context and the complexity of the events involved.
What is events that have the same probability?
They are "events that have the same probability". Nothing more, nothing less.
What events are such that the occurrence of one does not change the probability of other events?
Independent events.
Is it true that two dependent events can have the same probability of occurring?
Yes, it is possible for two dependent events to have the same probability of occurring. The probability of an event is dependent on the outcomes of other events, and it is influenced by the relationship between these events. So, it is conceivable for two dependent events to have equal probabilities.
Can independent events exist in reality?
Yes. Independent events can exist in reality. Dependent events means that one event has had an effect on the other. For instance, if we look at the probability of someone going to the shops, and the probability of them buying an apple, the latter is clearly dependent on the former. Independent events are simply events that don't have this connection. The probability of one does not influence or predict the probability of the other. For instance, if I studied the probability of you going to see a film on a particular day, and the probability of someone in China getting a hole in one in golf, these are very clearly independent events.
What do I call a probability that is based upon an event that has already occurred?
It can be called a "conditional probability", but the word "conditional" is irrelevant if the two events are independent.
What is the probability of getting 5 in rolling a die given that 6 has occurred already?
If it is a fair die and rolled fairly, the two events are independent so that the probability is 1/6.
What is the probability of an event that is affected by two or more different events called?
A dependent probability.
Are the historical events which have occurred extremely unlikely and what history has a higher probability of occurring?
Historical events which have occurred have a probability of 1. They are a certainty. This refers to the event itself, not some historian's or politician's interpretation of what happened. However, the probability that they will occur again depends on the event. Exact recurrence is impossible (probability = 0).
What is the relationship between conditional probability and the concept of statistical independence?
If events A and B are statistically indepnedent, then the conditional probability of A, given that B has occurred is the same as the unconditional probability of A. In symbolic terms, Prob(A|B) = Prob(A).
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.
Is there just one way of computing the probability of dependent events?
No, there isn't just one way of computing the probability of dependent events. One common method is to use the formula ( P(A \cap B) = P(A) \times P(B|A) ), where ( P(B|A) ) is the conditional probability of event B given that event A has occurred. Another approach involves constructing a probability tree or using joint probability tables, especially when dealing with multiple dependent events. The choice of method often depends on the context and the complexity of the events involved.
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 retelling stories of past events called?
Retelling stories of past events is often referred to as recounting or narrating events. It involves summarizing or describing events that have already occurred in a chronological order.
What is events that have the same probability?
They are "events that have the same probability". Nothing more, nothing less.
If the probability of two events occurring together is 0 the events are called .?
Independent events with a probability of zero
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%.
