A very good professional baseball player gets a hit about 35...

A very good professional baseball player gets a hit about $35 \%$ of the time over an entire season. After the player failed to hit safely in six straight at bats, a $1 \mathrm{V}$ commentator said, "He is due for a hit by the law of averages." Is that right? Why?

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Key Concepts

Law of Averages Misinterpretation

The concept sometimes referred to as the 'law of averages' is frequently misinterpreted to mean that outcomes will balance out in the short term, implying that a probability event is 'due' after a streak of opposing results. In reality, while large numbers may approximate the expected proportion, short-term variations are common, and past results do not dictate immediate future outcomes.

Gambler's Fallacy

The gambler's fallacy is the mistaken belief that after a series of similar outcomes, a contrasting outcome is 'due' to occur. This erroneous reasoning often leads to the misconception that a player is more likely to get a hit after several failures, even though each event is independent and the chances remain unchanged.

Independent Events

In probability theory, independent events are events whose outcomes have no influence on one another. When each batting attempt is considered an independent event, the outcome of the previous at bats does not affect the probability of the next hit. This means that the probability remains constant regardless of past outcomes.

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