Sample Space

Definition

The sample space of a probability trial is a list of all possible outcomes when the trial occurs.

Event 1: Flipping a Coin

The sample space of a coin flip is {Head, Tail}.

Use the applet below to guess the outcome of a coin flip. Are you feeling lucky?

If the result of 5 successive coin flips are all heads, is it more likely or less likely that the next flip will be tails?

The Gamblers Fallacy

Gamblers usually make the cognitive error that falsely assumes that past outcomes affect future outcomes. In reality, if it is a fair trial, the probability of each trial is independent of past outcomes. Just because there have been 5 successive heads in a row, does not change the probability of the next trial to be more or less likely heads.

However, if over a large sample size, a coin has shown a significant bias towards head, we could hypothesize that the coin may not be fair (equal chance of heads and tails) and go do the binomial test to determine if the deviation is significant.

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