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What is independent events in probability concepts?
The occurrence of one event does not affect the occurrence of the other event. Take for example tossing a coin. The first toss has no affect on the outcome of the second toss, so these events are independent.
If the probability of two events occurring together is 0 the events are called?
If the probability of two events occurring together is 0, the events are called mutually exclusive. This means that the occurrence of one event precludes the occurrence of the other, so they cannot happen at the same time. For example, flipping a coin can result in either heads or tails, but not both simultaneously.
Can two events be mutually exclusive and independent simultaneously?
No, two events cannot be mutually exclusive and independent simultaneously. Mutually exclusive events cannot occur at the same time, meaning the occurrence of one event excludes the possibility of the other. In contrast, independent events are defined such that the occurrence of one event does not affect the probability of the other occurring. Therefore, if two events are mutually exclusive, the occurrence of one event implies that the other cannot occur, which contradicts the definition of independence.
What is a true statement about mutually exclusive events?
Mutually exclusive events are events that cannot occur at the same time; the occurrence of one event precludes the occurrence of the other. For example, when flipping a coin, the outcomes of heads and tails are mutually exclusive because you cannot get both results in a single flip. In probability terms, the probability of both events occurring simultaneously is zero. If events A and B are mutually exclusive, then the probability of either A or B occurring is the sum of their individual probabilities: P(A or B) = P(A) + P(B).
When the occurrence of one event does not influence the occurrence of the other?
They are independent events.
What is independent events in probability concepts?
The occurrence of one event does not affect the occurrence of the other event. Take for example tossing a coin. The first toss has no affect on the outcome of the second toss, so these events are independent.
If the probability of two events occurring together is 0 the events are called?
If the probability of two events occurring together is 0, the events are called mutually exclusive. This means that the occurrence of one event precludes the occurrence of the other, so they cannot happen at the same time. For example, flipping a coin can result in either heads or tails, but not both simultaneously.
Can two events be mutually exclusive and independent simultaneously?
No, two events cannot be mutually exclusive and independent simultaneously. Mutually exclusive events cannot occur at the same time, meaning the occurrence of one event excludes the possibility of the other. In contrast, independent events are defined such that the occurrence of one event does not affect the probability of the other occurring. Therefore, if two events are mutually exclusive, the occurrence of one event implies that the other cannot occur, which contradicts the definition of independence.
What is a true statement about mutually exclusive events?
Mutually exclusive events are events that cannot occur at the same time; the occurrence of one event precludes the occurrence of the other. For example, when flipping a coin, the outcomes of heads and tails are mutually exclusive because you cannot get both results in a single flip. In probability terms, the probability of both events occurring simultaneously is zero. If events A and B are mutually exclusive, then the probability of either A or B occurring is the sum of their individual probabilities: P(A or B) = P(A) + P(B).
When the occurrence of one event does not influence the occurrence of the other?
They are independent events.
What are two events called when the occurrence of one event does not affect the occurrence of the other event?
Independent
Events for which the outcome of one event affects the probability of the other?
Dependent events.
What is events for which the outcome of one event does not affect the probability of the other?
Independent events.
What is independent and dependent when dealing with probability?
The event whose occurrence is not relying on other the other event is independent e.g the occurance of Head in a coin throw is not dependent on other side, the Tail, so it is an independent event. When two events are depending on each other in order to gain a required result, the events are said to be dependant.
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.
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.
Which is a pair of independent events?
Two events are independent if the outcome of one has no effect on the probability of the outcomes for the other.
