Independent trials in relationship to probability theory means that?
a. The outcome of each trial is totally independent from each other trial conducted
B. Each outcome has an indendent relationship to the whole
C. The outcome of each trial is dependent upon the previous but not the following
D. Influences of trials on the outcome are subtle overall
The outcome of each trial is totally independent from each other trial conducted
. Each outcome has an indendent relationship to the whole
The correct answer is:
a. The outcome of each trial is totally independent from each other trial conducted.
Independent trials in probability theory refer to a sequence of experiments or events where the outcome of each trial does not affect the outcome of any other trial. In other words, the occurrence or result of one trial has no influence on subsequent trials. Each trial is treated as a separate and unrelated event.
To determine if a sequence of events or trials are independent, you can consider the following:
1. Determine the nature of the events: If the outcome of each trial is influenced by previous or future trials, then the events are dependent. If the outcome of each trial is not influenced by any other trial, then the events are independent.
2. Assess conditional probabilities: If the probability of one event changes based on the occurrence or result of another event, then the events are dependent. If the probability of one event remains unchanged irrespective of other events, then the events are independent.
To understand the concept of independent trials, you can imagine flipping a fair coin. Each coin flip is an independent trial because the outcome of one flip does not affect the outcome of the next flip. Whether you get heads or tails on the first flip has no bearing on the second flip.
Remember, it is crucial to establish whether events or trials are independent or dependent when calculating probabilities and making predictions based on probability theory.