Final answer:
The Gambler's Fallacy is the misconception that prior outcomes affect future independent events, like believing a coin is 'due' to land on tails after several heads; it is often accompanied by confirmation bias, where people focus on outcomes that confirm their existing beliefs. The correct answer is option A).
Step-by-step explanation:
The term that describes the misconception that prior outcomes influence subsequent independent events, which is often illustrated by phenomena such as roulette, is known as The Gambler's Fallacy. This fallacy occurs when an individual falsely believes that if something happens less frequently than normal during some period, it will happen more frequently in the future, or vice versa. For example, if a coin has come up heads several times in a row, the gambler's fallacy would lead one to wrongly assume that tails must be 'due', ignoring the fact that each coin toss is statistically independent with a fair coin having an equal chance of landing heads or tails every time.
Further illustrating this concept, another cognitive bias, confirmation bias, often goes hand-in-hand with the gambler's fallacy. Confirmation bias leads individuals to pay more attention to outcomes that confirm their existing beliefs, such as thinking that a certain item of clothing is 'lucky' because they recall instances of winning while wearing it, while ignoring the losses.
Both the gambler's fallacy and confirmation bias can influence decision-making and problem-solving in negative ways by leading to a reliance on fallacious reasoning or misinformation, rather than on rational analysis and statistical probabilities.