Two events are _____________________ if the outcome of one trial does not influence or change the outcome of any other trial.

Question

BlackTom AI · Accepted Answer

Consider the principle described in probability theory: when the result of one trial does not alter the probabilities for outcomes in other trials, the trials are said to be independent.
In such a situation, the joint probability of two events equals the product of their individual probabilities, i.e., P(A and B) = P(A) × P(B). This reflects that knowledge of what happened in one trial provides no information about what will happen in another.
A common intuitive example is flipping a fair coin twice; the result of the first flip (heads or tails) does not change the likelihood of heads or tails on the second flip. The independence property can be contrasted with dependence, where the outcome of one trial affects the probabilities or outcomes of subsequent trials (for instance, drawing cards without replacement from a finite deck).
When a question states that the outcome of one trial does not influence or change the outcome of any other trial, the correct descriptor is that the events are independent, since their results do not alter each other’s likelihoods or outcomes.

Two events are _____________________ if the outcome of one trial does not influence or change the outcome of any other trial.简答题

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