Final answer:
True, past history has no effect on independent events as they do not influence each other's likelihood of occurring; each event's occurrence is independent of the past events.
Step-by-step explanation:
When dealing with independent events, it is true that past history has no effect. This concept is crucial in the field of probability and statistics, and it expresses the memoryless property for an exponential random variable X, where knowledge of what has occurred in the past does not affect future probabilities.
For two events to be categorized as independent, the occurrence of one event should not alter the likelihood of the other.
This can be summarized through the following properties: P(A AND B) = P(A)P(B), and P(B|A) = P(B), which imply that the probability of both events happening is equal to the product of their individual probabilities, and the probability of event B given that event A has happened is the same as the probability of event B occurring by itself.
Gambler's fallacy is a common example of confusion over independent events where one might erroneously think that past events affect future outcomes in processes like a coin toss.
In reality, each toss is independent of the others. Therefore, the statement 'When dealing with independent events, past history has no effect' is true.