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An independent probability is a probability that is not based on any other event.
An example of an independent probability is a coin toss. Each toss is independent, i.e. not related to, any prior coin toss.
An example of a dependent probability is the probability of drawing a second Ace from a deck of cards. The probability of the second Ace is dependent on whether or not a first Ace was drawn or not. (You can generalize this to any two cards because the sample space for the first card is 52, while the sample space for the second card is 51.)
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Is the probability of two independent events occurring together the same as the probability of each occurring alone?
No, the combined probability is the product of the probability of their separate occurrances.
Is probability independent?
It may or may not be - it depends on the events.
The probability of two independent events occurring together is the of the probability of each event occurring separately?
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What is the probability a set of outcomes?
The probability depends on the nature of the outcomes in the set: whether or not they are mutually exclusive, independent.
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.
